Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

angela210793 Group Title

Is there anyone who can explain me the range of a matrix???

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not sure what it is but this should give u a head start to what it means http://en.wikipedia.org/wiki/Column_space

    • 2 years ago
  2. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    wht i do not understand is how u make the transformations ...how do u know tht u change the places of x-row with y row...:(:(:(

    • 2 years ago
  3. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    To find the range of a matrix, just reduce it into row echelon form, and count the number of non zero rows. The number of non zero rows is the range of the matrix

    • 2 years ago
  4. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh! that thing, I am afraid you will have to figure that out yourself.

    • 2 years ago
  5. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But the key is to practice more and more reduction..

    • 2 years ago
  6. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    myself????? :O I've tried to...but i don't get it :((((

    • 2 years ago
  7. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I can help you out with a rough algorithm or something like "steps to perform", but still you will need to practice using that algorithm.

    • 2 years ago
  8. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ok....can u explain me how u solve aproblem like this in twiddla??

    • 2 years ago
  9. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Why not here..?

    • 2 years ago
  10. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But before that let me make sure, you want me to teach you how to reduce a matrix into row echelon form, right?

    • 2 years ago
  11. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yea ok ....

    • 2 years ago
  12. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So will I post an example? Or you will post yours

    • 2 years ago
  13. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I'll post one |dw:1329561659776:dw|

    • 2 years ago
  14. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    OK, now tell me what do you feel you must first do, and why?

    • 2 years ago
  15. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I have no idea at all :(((

    • 2 years ago
  16. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    OK, now you have to reduce it to something like |dw:1329561739686:dw|

    • 2 years ago
  17. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    With zeros in all the empty spaces, right?

    • 2 years ago
  18. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yea tht's smth i know...

    • 2 years ago
  19. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So start by making the top left corner 1

    • 2 years ago
  20. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You can do that by two methods, 1. Bring the lowest row to the top, 2. Divide the first column by 3

    • 2 years ago
  21. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    The first method seems easy

    • 2 years ago
  22. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I just exchanged row 1, and row 3

    • 2 years ago
  23. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    now u have to make 4 in the 3rd row 1 right?

    • 2 years ago
  24. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh no, there is another, just let me write it fresh...

    • 2 years ago
  25. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what happened to the 2 at the right corner?

    • 2 years ago
  26. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329562219705:dw|

    • 2 years ago
  27. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329562156101:dw|

    • 2 years ago
  28. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Right!

    • 2 years ago
  29. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Now again think, to make this new matrix similar to |dw:1329562260442:dw|

    • 2 years ago
  30. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    .....you need to make the first element in the 2nd row zero.

    • 2 years ago
  31. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i think u'll get a |dw:1329562374039:dw| won't you???

    • 2 years ago
  32. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i.e. the circled element |dw:1329562329966:dw|

    • 2 years ago
  33. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Sorry, you lost me.. but did you understand what I meant?

    • 2 years ago
  34. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yea yea i understood xD just tell me smth u make a diagonal =1 first and then 0 the other elements??

    • 2 years ago
  35. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Right!

    • 2 years ago
  36. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So the next step would be to subtract 2 times row-1 from row-2. Could you follow me?

    • 2 years ago
  37. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I mean do you feel why I am doing that?

    • 2 years ago
  38. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    no.....don't u have to make the 4 in the third row 0 first???? O.o

    • 2 years ago
  39. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Which one? Can you circle it for me?

    • 2 years ago
  40. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329562705396:dw|

    • 2 years ago
  41. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    No, not at all. All you need to do is keep in mind the picture I gave you and proceed accordingly

    • 2 years ago
  42. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    By picture I meant, the matrix with 1 on the diagonals and 0s elsewhere.

    • 2 years ago
  43. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    see.... wht u gave me is |dw:1329562830135:dw| and u have 4 ones in there(a diagonal with 4 elements) ...this isn't a square matrix to get tht....O.o and u said u'd do 1(ones) all the elements of the diagonal first then 0 the other elements......

    • 2 years ago
  44. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I am sorry, if you got that impression, but that is not exactly what I meant. I meant something of that sort that doesn't necessarily imply that it has to be 4 squared etc etc.

    • 2 years ago
  45. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I mean after reduction your picture will look something like that funny picture.

    • 2 years ago
  46. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ahhhhhhhhhhhhhhhaaaaaaaaaaaaaaa......I'm sorry then :/ keep going....why would u multiply first row with 2 and then subtract it to row 2

    • 2 years ago
  47. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Just to make it look like that funny picture...

    • 2 years ago
  48. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You will end up with something like |dw:1329563098194:dw|

    • 2 years ago
  49. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    tht's wht i meant by this pic |dw:1329563199692:dw|

    • 2 years ago
  50. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So what do you feel? Don't you feel that once you have got the first element in the first row 1, you should now start thinking about making the one just below it zero.

    • 2 years ago
  51. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I really don't understand that notation of yours, but do you understand mine?

    • 2 years ago
  52. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ;)

    • 2 years ago
  53. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    hahhaha...yea yea xD

    • 2 years ago
  54. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So just tell me, do you feel why I want to make the element just below 1, zero?

    • 2 years ago
  55. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry to barge in but is it just any diagonal or just the diagonal that cuts through starting with the first number?

    • 2 years ago
  56. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i mean the diagonal that must be all 1's....

    • 2 years ago
  57. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Any diagonal...

    • 2 years ago
  58. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes yes I get this I'm gonna ask u smth just pls don't get angry....don't u have to make |dw:1329563400348:dw| this 1 first????

    • 2 years ago
  59. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Well, I never learnt it that way...:)

    • 2 years ago
  60. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    May be that is some other method.

    • 2 years ago
  61. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ahhhhaaaaaaaaaa...ok then...u do wht u know...:)

    • 2 years ago
  62. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    math is a very clumsy road, u end up at the same destination

    • 2 years ago
  63. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i wasn't ending up anywhere with this problem :P

    • 2 years ago
  64. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    did u read the manual/instruction/algorithm to solving this problem?

    • 2 years ago
  65. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329563439879:dw|

    • 2 years ago
  66. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Is that clear?

    • 2 years ago
  67. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    wht did u do in there?????

    • 2 years ago
  68. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    OMG!!! I'm hopeless x( :(:(

    • 2 years ago
  69. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    R2-2R1

    • 2 years ago
  70. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    got it or not?

    • 2 years ago
  71. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    wasn't the first element of the 2nd row supposed to b zero??? 2-(2*1)=2-2=0

    • 2 years ago
  72. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh, does that thing look like 6, its actually 0..

    • 2 years ago
  73. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    lol

    • 2 years ago
  74. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ahhhhaaaaa...ok then xD

    • 2 years ago
  75. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Next you need to turn the first element in the third row equal to zero

    • 2 years ago
  76. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    would tht be R3-3R1???

    • 2 years ago
  77. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wait so u do 1 0 0 column by column, as in one column after the other?

    • 2 years ago
  78. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329563860051:dw|

    • 2 years ago
  79. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Sasogeek is right!

    • 2 years ago
  80. sasogeek Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    1000 0100 0010 u should end up with this... right?

    • 2 years ago
  81. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Exactly, but it may look a little different, but something similar to that.. P.S. angela210793 you typed the right notation

    • 2 years ago
  82. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ok....no now u have to make -3 in the 2nd column zero...how do u do tht???

    • 2 years ago
  83. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    First of all, can you check, if I did the calculations correct?

    • 2 years ago
  84. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    hang on

    • 2 years ago
  85. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329564323164:dw|

    • 2 years ago
  86. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Thats right! I think

    • 2 years ago
  87. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i think so too O.o.....wht's next?

    • 2 years ago
  88. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So the matrix which we now have is |dw:1329564404847:dw|

    • 2 years ago
  89. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Now this particular problem was prepared in such a way, that we ended up with the 2nd and third row as equal

    • 2 years ago
  90. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But that is a nice case, it will not happen always.

    • 2 years ago
  91. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    In cases where it doesn't happen, you next intention would be to make the circled element equal to 1|dw:1329564569074:dw|

    • 2 years ago
  92. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Once the circle element is made 1, you will attempt to make all the elements below it equal to 0

    • 2 years ago
  93. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    can we multiply the second row with 1/7???

    • 2 years ago
  94. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, that is exactly what you should have done if you were a computer.

    • 2 years ago
  95. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can.. but it would be complicated

    • 2 years ago
  96. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    try avoiding fractions form..

    • 2 years ago
  97. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    then what?? O.o

    • 2 years ago
  98. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But being a human you can see, that you can subtract the second row from the third, and write it down in the third row

    • 2 years ago
  99. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    And that will make the whole of third row equal to zero

    • 2 years ago
  100. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ohhhhhh...well i'm not a random person...I think like a computer :P

    • 2 years ago
  101. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1329564788814:dw|

    • 2 years ago
  102. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    7 is still 7...wht now?

    • 2 years ago
  103. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So now clearly you have two non zero rows, you can now say, that the range is 2

    • 2 years ago
  104. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    R3=R3+R2

    • 2 years ago
  105. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    :O wht??? how was tht ..can u explain me once again please ???

    • 2 years ago
  106. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ops it is R3=R3-R2

    • 2 years ago
  107. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Just as I told you this was a nice problem. Real problems won't be like this. Here without any further reduction, it is visible, that no matter what you do, you can never make any of R2 or R1 zero... so there are two non zero rows. so t he range is 2

    • 2 years ago
  108. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Hmmmmmmmmmmmm......ok.... Thank u very much :))))))))))) all of u, especially 2bornot2b :)) Gosh...How can u b so patient????

    • 2 years ago
  109. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont understand what is range?

    • 2 years ago
  110. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Here is a good problem

    • 2 years ago
  111. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i don't think it is good :P

    • 2 years ago
  112. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I meant it gives you the feel of what you need to do in real problems

    • 2 years ago
  113. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok now i understad what is range.. :)

    • 2 years ago
  114. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    And you can see in the reduction, things go in the same algorithm as I mentioned

    • 2 years ago
  115. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so for the attachement given.. the range is 3 right?

    • 2 years ago
  116. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Right xilem

    • 2 years ago
  117. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok now i understand.. but what it is for?

    • 2 years ago
  118. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Something very deep xilem, its for actually solving linear equation.

    • 2 years ago
  119. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yea...why do we need these kind of problems in business? O.o

    • 2 years ago
  120. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But now it seems like a game

    • 2 years ago
  121. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    quoted earlier( wht i do not understand is how u make the transformations ...how do u know tht u change the places of x-row with y row...:(:(:( ) -this is call transpose

    • 2 years ago
  122. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Say I have 10 equations and each equations have 10 unknown, how are you going to solve it?

    • 2 years ago
  123. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so after having done all these things, I mean whatever you are studying, you will be able to solve linear equations without any effort.

    • 2 years ago
  124. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i know wht transposed matrix is....i didn't know why u changed x with y and why not x with z for example

    • 2 years ago
  125. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    crammer's rule :D

    • 2 years ago
  126. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    But how did crammer invent that? This is all behind the scenes

    • 2 years ago
  127. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i think all these things r unnecessary.....

    • 2 years ago
  128. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I'm going to do my hws now...hopefully i'll solve them :) thnx a lot :)

    • 2 years ago
  129. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hurmm... sorry can u show me example of that in cramers rule?

    • 2 years ago
  130. 2bornot2b Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I said that you learn linear algebra to be able to solve linear equations, and cramers rule is just a product of linear algebra, so it directly is not a problem which can be used to show the application of cramers rule.

    • 2 years ago
  131. xilem89 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no i mean for the cramers rule (.i didn't know why u changed x with y and why not x with z for example ) can u show me example?

    • 2 years ago
  132. angela210793 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    this is how I've been taught cramer's rule |dw:1329576915751:dw|

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.