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

shivam_bhalla

Ok. A determinants question(Link below). What I have done? Well, I tried Row1 = Row 1+Row 2+row 3 but nothing great. Can you guys guide me to get the answer??

  • one year ago
  • one year ago

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

    http://mypat.in/PaperImages/3/425/Q_4_004.gif

    • one year ago
  2. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 0

    can you factor all of the elements

    • one year ago
  3. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @UnkleRhaukus ,how exactly??

    • one year ago
  4. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\Delta=\left|\begin{array}\\1+a^2+a^4&1+ab+a^2b^2&1+ac+a^2c^2\\1+ab+a^2b^2&1+b^2+b^4&1+bc+b^2c^2\\1+ac+a^2c^2&1+bc+b^2c^2&1+c^2+c^4\end{array}\right|\]

    • one year ago
  5. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah maybe not, i really dont want to do it the normal way

    • one year ago
  6. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Normal way-->never :D It would take ages :P

    • one year ago
  7. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 0

    but it would work in theory, but i would make about ten mistakes

    • one year ago
  8. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    I am sure you play around with determinant properties like Row1 = Row 1 + Row 2+Row3 . I mean some tweaking of that sort

    • one year ago
  9. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @apoorvk

    • one year ago
  10. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    can we just do it the foolish way?

    • one year ago
  11. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm, tried C1 - C2?

    • one year ago
  12. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @inkyvoyd Sorry, please, In my exam I have only 3 min(max) to solve this question @apoorvk ,let me give it a try and get back to you

    • one year ago
  13. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @apoorvk , I did that. But nothing can be taken common out :(

    • one year ago
  14. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm going to try this problem

    • one year ago
  15. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    Have no fear, for inky is here!

    • one year ago
  16. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 1

    I got common stuff out through C1-C2 and C2-C3. but, i am still stuck with a trinomial in each ditch..

    • one year ago
  17. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    @shivam_bhalla I HAVE AN IDEA

    • one year ago
  18. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    aei+bfg+cdh-ceg-bdi-afh =a(ei-fh)+b(fg-dj)+c(dg-eg)

    • one year ago
  19. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    b=d f=h

    • one year ago
  20. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    c=g

    • one year ago
  21. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    aei+bfg+cdh-ceg-bdi-afh aei+bf^2+cbf-ec^2-ah^2

    • one year ago
  22. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @inkyvoyd , what is a,b,c,d,e,f,g?? Are you expanding the determinant??

    • one year ago
  23. inkyvoyd
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm wikipediaing, and not making any progress.

    • one year ago
  24. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    LOL. @ "wikipediaing" . :)

    • one year ago
  25. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 1

    wolfram!!!

    • one year ago
  26. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    How to wolfram this ??

    • one year ago
  27. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @radar sir, any clue ??

    • one year ago
  28. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    factor out the commons!!!

    • one year ago
  29. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX , how exactly ?? I mean row wise or column wise. And moreover, what to factor out ??

    • one year ago
  30. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    lol ... factoring out would lead to 3 more matrices ..thats ugly... must be some pattern!!

    • one year ago
  31. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh. Now get what you meant by factoring .:P I tried that too and observed what you said :)

    • one year ago
  32. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    it seems transpose of itself!!

    • one year ago
  33. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1336584742255:dw| this is how far i got then..

    • one year ago
  34. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    try making these types to a^4 + a^2 + 1 => a^6 - 1 (ab)^2 + (ab) + 1 => (ab)^3 - 1 ... not sure if it can help ... too tired!!!

    • one year ago
  35. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    This problem really is trollling me very badly :( I will solve this problem before going to sleeep

    • one year ago
  36. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    if you find let met know!!

    • one year ago
  37. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    Oo ...we can drop all ones!!

    • one year ago
  38. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    Oo ... i got zero!! LOL

    • one year ago
  39. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    @shivam_bhalla you still there??

    • one year ago
  40. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

    • one year ago
  41. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    looks like it got it correct http://www.wolframalpha.com/input/?i=det+{{1%2Ba^2%2Ba^4%2C+1+%2B+%28ab%29+%2B+%28ab%29^2%2C+1+%2B+%28ac%29+%2B+%28ac%29^2}%2C++%09{1+%2B+%28ab%29+%2B+%28ab%29^2%2C+1%2Bb^2%2Bb^4%2C+1+%2B+bc+%2B+%28bc%29^2}%2C++%09{1+%2B+%28ac%29+%2B+%28ac%29^2%2C+1+%2B+bc+%2B+%28bc%29^2%2C+1+%2B+c^2+%2B+c^4}}

    • one year ago
  42. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    LOL @experimentX , that is doing it the long way Atleast I know the answer know. :) Thanks for typing out the huge question on wolframalpha :)

    • one year ago
  43. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    No .. i know the shortcut too!!

    • one year ago
  44. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    actually i verified answer at wolframalpha!!

    • one year ago
  45. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. Just tell me the method and not the steps because that would literally troll you

    • one year ago
  46. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX

    • one year ago
  47. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    take out all ones!! sine they will have same values on row .. they will be zero ..

    • one year ago
  48. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, didn't get you @experimentX

    • one year ago
  49. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1336588777520:dw|

    • one year ago
  50. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1336588827490:dw|

    • one year ago
  51. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1336588893052:dw|

    • one year ago
  52. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    i'm not sure how far everyone has got so far but first thoughts: setting a = b we can see that the determinant is zero as R1 = R2 hence (a-b) must be a factor

    • one year ago
  53. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    whenever matrix has same elements on row or column ... determinant is zero.

    • one year ago
  54. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    and by symmetry (b-c) and (a-c) are

    • one year ago
  55. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX , I never studied that. I only studied that if two rows or 2 colums are proportional to each other, then the determinant of the matrix is zero @eigenschmeigen , Very logical approach which eliminates option (a) for us :)

    • one year ago
  56. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    ;D

    • one year ago
  57. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    proportional ->eg R1 = kR2 so k = 1 is a specific case

    • one year ago
  58. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    Oo ... then i must have mistake!!

    • one year ago
  59. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    no its correct

    • one year ago
  60. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    if R1 = R2 then det(M) = 0

    • one year ago
  61. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @eigenschmeigen , there is no R1=R2 in @experimentX 's proof

    • one year ago
  62. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh my mistake ... i got the answer in fluke

    • one year ago
  63. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX , I wish these flukes come for me too in my exam :P

    • one year ago
  64. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    LOL ... i haven't reviewed matrices in long time!! best of luck if you are having exams right now!!

    • one year ago
  65. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    LOL. I have college entrance exam's right now :P

    • one year ago
  66. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    *exams

    • one year ago
  67. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    is this problem solved or still at large? i can have a proper go now i have a pen

    • one year ago
  68. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    The problem as of now is unsolved @eigenschmeigen

    • one year ago
  69. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay ... i think i got this time!! you can use same technique to reduce matrix!!

    • one year ago
  70. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1336589808195:dw|

    • one year ago
  71. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    and then it's simplification!!

    • one year ago
  72. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    apply operation as above!!! |dw:1336589933207:dw|

    • one year ago
  73. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    same as you had in your second place!! -- minus --- one

    • one year ago
  74. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1336590227531:dw|

    • one year ago
  75. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    • one year ago
    1 Attachment
  76. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1336590458004:dw| It can be proved!!

    • one year ago
  77. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX , I will try and let you know in 5-10 minutes @experimentX

    • one year ago
  78. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    okay ... it's just simplification after that. factoring out common factor ... then again you will have 1's and then use same technique ... in the end you will get two linearly dependent columns!! then it will be zero!!

    • one year ago
  79. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    its B

    • one year ago
  80. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    i'm just checking my working

    • one year ago
  81. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i write matrices on here?

    • one year ago
  82. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    @eigenschmeigen , your answer is right. You can use drawing doard :)

    • one year ago
  83. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    ok gimme a sec

    • one year ago
  84. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    *board.

    • one year ago
  85. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    i like the equation writer, i'm quicker that way: \[\left[\begin{matrix}1+a^2 + a^4 & 1+ ab+a^2b^2 & 1 +ac +a^2c^2 \\ 1 + ab +a^2b^2 & 1+b^2 + b^4 & 1 +ac +a^2c^2 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]

    • one year ago
  86. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    letting a = b we get R1 = R2 letting b = c we get R2 = R3 so the operations to do are R1- R2 = R1' and R2 - R3 = R2'

    • one year ago
  87. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\left[\begin{matrix}a^4 + a^2 - ab - a^2b^2 & a^2b^2 + ab -b^2 -b^4 & a^2c^2 + ac - bc - b^2c^2 \\ a^2b^2 + ab -ac -a^2c^2 & b^4 + b^2 - bc - b^2c^2 & b^2c^2 + bc -c^2 - c^4 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]

    • one year ago
  88. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    factor out (a-b)(b-c)

    • one year ago
  89. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    \[(a-b)(b-c)\left[\begin{matrix}a^3 + a +ba^2 & b^3 + b + ab^2 & c(ac+bc+1) \\ a(ac+ab+1) & b^3 + b +cb^2 & c^3 + c + bc^2 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]

    • one year ago
  90. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    letting a = b we now have C1 = C2 so we can see that (a-b) is again a factor. this narrows it down to B as we will have (a-b)^2 in our answer

    • one year ago
  91. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    you can continue to factorise if you want, but this is sufficient to get the right option.

    • one year ago
  92. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    its not said in many textbooks but i find using factor theorem is really useful for factorising determinants, as it tells us an operation that will result in something we can factor

    • one year ago
  93. shivam_bhalla
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you @eigenschmeigen and @experimentX for both of your solutions :D Thanks for taking your time :)

    • one year ago
  94. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    no problem, love matrices :)

    • one year ago
  95. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    looks like i didn't get that right ... i'm embarrassed. looks like 'linear algebra' is the first thing i should do after i'm done with calc

    • one year ago
  96. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 1

    what else does linear algebra cover?

    • one year ago
  97. experimentX
    Best Response
    You've already chosen the best response.
    Medals 2

    well ... all forgot!! let's see ... i have a book here. Linear algebra - Serge Lang Vectors, Vector spaces, Matirces, Linear mappings, Linear mappings and matrices, .... Groups, Rings, Convex Sets ... Appendix I thought \( \Delta\) on wolfram was the answer!!

    • one year 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.