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angela210793

  • 2 years ago

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

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  1. sasogeek
    • 2 years ago
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    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. angela210793
    • 2 years ago
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    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...:(:(:(

  3. 2bornot2b
    • 2 years ago
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    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

  4. 2bornot2b
    • 2 years ago
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    Oh! that thing, I am afraid you will have to figure that out yourself.

  5. 2bornot2b
    • 2 years ago
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    But the key is to practice more and more reduction..

  6. angela210793
    • 2 years ago
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    myself????? :O I've tried to...but i don't get it :((((

  7. 2bornot2b
    • 2 years ago
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    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.

  8. angela210793
    • 2 years ago
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    ok....can u explain me how u solve aproblem like this in twiddla??

  9. 2bornot2b
    • 2 years ago
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    Why not here..?

  10. 2bornot2b
    • 2 years ago
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    But before that let me make sure, you want me to teach you how to reduce a matrix into row echelon form, right?

  11. angela210793
    • 2 years ago
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    yea ok ....

  12. 2bornot2b
    • 2 years ago
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    So will I post an example? Or you will post yours

  13. angela210793
    • 2 years ago
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    I'll post one |dw:1329561659776:dw|

  14. 2bornot2b
    • 2 years ago
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    OK, now tell me what do you feel you must first do, and why?

  15. angela210793
    • 2 years ago
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    I have no idea at all :(((

  16. 2bornot2b
    • 2 years ago
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    OK, now you have to reduce it to something like |dw:1329561739686:dw|

  17. 2bornot2b
    • 2 years ago
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    With zeros in all the empty spaces, right?

  18. angela210793
    • 2 years ago
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    yea tht's smth i know...

  19. 2bornot2b
    • 2 years ago
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    So start by making the top left corner 1

  20. 2bornot2b
    • 2 years ago
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    You can do that by two methods, 1. Bring the lowest row to the top, 2. Divide the first column by 3

  21. 2bornot2b
    • 2 years ago
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    The first method seems easy

  22. 2bornot2b
    • 2 years ago
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    I just exchanged row 1, and row 3

  23. angela210793
    • 2 years ago
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    now u have to make 4 in the 3rd row 1 right?

  24. 2bornot2b
    • 2 years ago
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    Oh no, there is another, just let me write it fresh...

  25. sasogeek
    • 2 years ago
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    what happened to the 2 at the right corner?

  26. angela210793
    • 2 years ago
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    |dw:1329562219705:dw|

  27. 2bornot2b
    • 2 years ago
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    |dw:1329562156101:dw|

  28. 2bornot2b
    • 2 years ago
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    Right!

  29. 2bornot2b
    • 2 years ago
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    Now again think, to make this new matrix similar to |dw:1329562260442:dw|

  30. 2bornot2b
    • 2 years ago
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    .....you need to make the first element in the 2nd row zero.

  31. angela210793
    • 2 years ago
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    i think u'll get a |dw:1329562374039:dw| won't you???

  32. 2bornot2b
    • 2 years ago
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    i.e. the circled element |dw:1329562329966:dw|

  33. 2bornot2b
    • 2 years ago
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    Sorry, you lost me.. but did you understand what I meant?

  34. angela210793
    • 2 years ago
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    yea yea i understood xD just tell me smth u make a diagonal =1 first and then 0 the other elements??

  35. 2bornot2b
    • 2 years ago
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    Right!

  36. 2bornot2b
    • 2 years ago
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    So the next step would be to subtract 2 times row-1 from row-2. Could you follow me?

  37. 2bornot2b
    • 2 years ago
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    I mean do you feel why I am doing that?

  38. angela210793
    • 2 years ago
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    no.....don't u have to make the 4 in the third row 0 first???? O.o

  39. 2bornot2b
    • 2 years ago
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    Which one? Can you circle it for me?

  40. angela210793
    • 2 years ago
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    |dw:1329562705396:dw|

  41. 2bornot2b
    • 2 years ago
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    No, not at all. All you need to do is keep in mind the picture I gave you and proceed accordingly

  42. 2bornot2b
    • 2 years ago
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    By picture I meant, the matrix with 1 on the diagonals and 0s elsewhere.

  43. angela210793
    • 2 years ago
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    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......

  44. 2bornot2b
    • 2 years ago
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    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.

  45. 2bornot2b
    • 2 years ago
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    I mean after reduction your picture will look something like that funny picture.

  46. angela210793
    • 2 years ago
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    ahhhhhhhhhhhhhhhaaaaaaaaaaaaaaa......I'm sorry then :/ keep going....why would u multiply first row with 2 and then subtract it to row 2

  47. 2bornot2b
    • 2 years ago
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    Just to make it look like that funny picture...

  48. 2bornot2b
    • 2 years ago
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    You will end up with something like |dw:1329563098194:dw|

  49. angela210793
    • 2 years ago
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    tht's wht i meant by this pic |dw:1329563199692:dw|

  50. 2bornot2b
    • 2 years ago
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    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.

  51. 2bornot2b
    • 2 years ago
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    I really don't understand that notation of yours, but do you understand mine?

  52. 2bornot2b
    • 2 years ago
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    ;)

  53. angela210793
    • 2 years ago
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    hahhaha...yea yea xD

  54. 2bornot2b
    • 2 years ago
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    So just tell me, do you feel why I want to make the element just below 1, zero?

  55. sasogeek
    • 2 years ago
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    sorry to barge in but is it just any diagonal or just the diagonal that cuts through starting with the first number?

  56. sasogeek
    • 2 years ago
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    i mean the diagonal that must be all 1's....

  57. 2bornot2b
    • 2 years ago
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    Any diagonal...

  58. angela210793
    • 2 years ago
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    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????

  59. 2bornot2b
    • 2 years ago
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    Well, I never learnt it that way...:)

  60. 2bornot2b
    • 2 years ago
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    May be that is some other method.

  61. angela210793
    • 2 years ago
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    ahhhhaaaaaaaaaa...ok then...u do wht u know...:)

  62. sasogeek
    • 2 years ago
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    math is a very clumsy road, u end up at the same destination

  63. angela210793
    • 2 years ago
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    i wasn't ending up anywhere with this problem :P

  64. sasogeek
    • 2 years ago
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    did u read the manual/instruction/algorithm to solving this problem?

  65. 2bornot2b
    • 2 years ago
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    |dw:1329563439879:dw|

  66. 2bornot2b
    • 2 years ago
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    Is that clear?

  67. angela210793
    • 2 years ago
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    wht did u do in there?????

  68. angela210793
    • 2 years ago
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    OMG!!! I'm hopeless x( :(:(

  69. 2bornot2b
    • 2 years ago
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    R2-2R1

  70. 2bornot2b
    • 2 years ago
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    got it or not?

  71. angela210793
    • 2 years ago
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    wasn't the first element of the 2nd row supposed to b zero??? 2-(2*1)=2-2=0

  72. 2bornot2b
    • 2 years ago
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    Oh, does that thing look like 6, its actually 0..

  73. 2bornot2b
    • 2 years ago
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    lol

  74. angela210793
    • 2 years ago
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    ahhhhaaaaa...ok then xD

  75. 2bornot2b
    • 2 years ago
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    Next you need to turn the first element in the third row equal to zero

  76. angela210793
    • 2 years ago
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    would tht be R3-3R1???

  77. sasogeek
    • 2 years ago
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    wait so u do 1 0 0 column by column, as in one column after the other?

  78. 2bornot2b
    • 2 years ago
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    |dw:1329563860051:dw|

  79. 2bornot2b
    • 2 years ago
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    Sasogeek is right!

  80. sasogeek
    • 2 years ago
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    1000 0100 0010 u should end up with this... right?

  81. 2bornot2b
    • 2 years ago
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    Exactly, but it may look a little different, but something similar to that.. P.S. angela210793 you typed the right notation

  82. angela210793
    • 2 years ago
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    ok....no now u have to make -3 in the 2nd column zero...how do u do tht???

  83. 2bornot2b
    • 2 years ago
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    First of all, can you check, if I did the calculations correct?

  84. angela210793
    • 2 years ago
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    hang on

  85. angela210793
    • 2 years ago
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    |dw:1329564323164:dw|

  86. 2bornot2b
    • 2 years ago
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    Thats right! I think

  87. angela210793
    • 2 years ago
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    i think so too O.o.....wht's next?

  88. 2bornot2b
    • 2 years ago
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    So the matrix which we now have is |dw:1329564404847:dw|

  89. 2bornot2b
    • 2 years ago
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    Now this particular problem was prepared in such a way, that we ended up with the 2nd and third row as equal

  90. 2bornot2b
    • 2 years ago
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    But that is a nice case, it will not happen always.

  91. 2bornot2b
    • 2 years ago
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    In cases where it doesn't happen, you next intention would be to make the circled element equal to 1|dw:1329564569074:dw|

  92. 2bornot2b
    • 2 years ago
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    Once the circle element is made 1, you will attempt to make all the elements below it equal to 0

  93. angela210793
    • 2 years ago
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    can we multiply the second row with 1/7???

  94. 2bornot2b
    • 2 years ago
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    Yes, that is exactly what you should have done if you were a computer.

  95. xilem89
    • 2 years ago
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    can.. but it would be complicated

  96. xilem89
    • 2 years ago
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    try avoiding fractions form..

  97. angela210793
    • 2 years ago
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    then what?? O.o

  98. 2bornot2b
    • 2 years ago
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    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

  99. 2bornot2b
    • 2 years ago
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    And that will make the whole of third row equal to zero

  100. angela210793
    • 2 years ago
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    ohhhhhh...well i'm not a random person...I think like a computer :P

  101. 2bornot2b
    • 2 years ago
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    |dw:1329564788814:dw|

  102. angela210793
    • 2 years ago
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    7 is still 7...wht now?

  103. 2bornot2b
    • 2 years ago
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    So now clearly you have two non zero rows, you can now say, that the range is 2

  104. xilem89
    • 2 years ago
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    R3=R3+R2

  105. angela210793
    • 2 years ago
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    :O wht??? how was tht ..can u explain me once again please ???

  106. xilem89
    • 2 years ago
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    ops it is R3=R3-R2

  107. 2bornot2b
    • 2 years ago
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    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

  108. angela210793
    • 2 years ago
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    Hmmmmmmmmmmmm......ok.... Thank u very much :))))))))))) all of u, especially 2bornot2b :)) Gosh...How can u b so patient????

  109. xilem89
    • 2 years ago
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    i dont understand what is range?

  110. 2bornot2b
    • 2 years ago
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    Here is a good problem

  111. angela210793
    • 2 years ago
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    i don't think it is good :P

  112. 2bornot2b
    • 2 years ago
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    I meant it gives you the feel of what you need to do in real problems

  113. xilem89
    • 2 years ago
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    ok now i understad what is range.. :)

  114. 2bornot2b
    • 2 years ago
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    And you can see in the reduction, things go in the same algorithm as I mentioned

  115. xilem89
    • 2 years ago
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    so for the attachement given.. the range is 3 right?

  116. 2bornot2b
    • 2 years ago
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    Right xilem

  117. xilem89
    • 2 years ago
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    ok now i understand.. but what it is for?

  118. 2bornot2b
    • 2 years ago
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    Something very deep xilem, its for actually solving linear equation.

  119. angela210793
    • 2 years ago
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    yea...why do we need these kind of problems in business? O.o

  120. 2bornot2b
    • 2 years ago
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    But now it seems like a game

  121. xilem89
    • 2 years ago
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    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

  122. 2bornot2b
    • 2 years ago
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    Say I have 10 equations and each equations have 10 unknown, how are you going to solve it?

  123. 2bornot2b
    • 2 years ago
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    so after having done all these things, I mean whatever you are studying, you will be able to solve linear equations without any effort.

  124. angela210793
    • 2 years ago
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    i know wht transposed matrix is....i didn't know why u changed x with y and why not x with z for example

  125. angela210793
    • 2 years ago
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    crammer's rule :D

  126. 2bornot2b
    • 2 years ago
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    But how did crammer invent that? This is all behind the scenes

  127. angela210793
    • 2 years ago
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    i think all these things r unnecessary.....

  128. angela210793
    • 2 years ago
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    I'm going to do my hws now...hopefully i'll solve them :) thnx a lot :)

  129. xilem89
    • 2 years ago
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    hurmm... sorry can u show me example of that in cramers rule?

  130. 2bornot2b
    • 2 years ago
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    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.

  131. xilem89
    • 2 years ago
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    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?

  132. angela210793
    • 2 years ago
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    this is how I've been taught cramer's rule |dw:1329576915751:dw|

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