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iop360

  • 2 years ago

Express the inverse of the following matrix (assuming it exists) as a matrix containing expressions in terms of k. -3 0 k 12 8 16 4 2 4

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  1. zzr0ck3r
    • 2 years ago
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    um you gave a list of numbers that in no way resembles a matrix

  2. iop360
    • 2 years ago
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    \[\left[\begin{matrix}3 & 0 & k \\ 12 & 8 & 16\\ 4 & 2 & 4\end{matrix}\right]^{-1}\]

  3. zzr0ck3r
    • 2 years ago
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    can you reduce it to I?

  4. iop360
    • 2 years ago
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    i think so

  5. iop360
    • 2 years ago
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    i write where i am write now

  6. zzr0ck3r
    • 2 years ago
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    k brb wife just got home.

  7. iop360
    • 2 years ago
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    this is just the coefficient matrix\[\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 2\\ 0 & 0 & k\end{matrix}\right]\]

  8. CliffSedge
    • 2 years ago
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    Use Gauss-Jordan elimination on \[\left[\begin{matrix}3 & 0 & k & 1 & 0 & 0\\ 12 & 8 & 16 & 0 & 1 & 0\\ 4 & 2 & 4 & 0 & 0 & 1\end{matrix}\right]\] That's how I do it. (There's probably an easier way..)

  9. iop360
    • 2 years ago
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    yes i started w/ that

  10. CliffSedge
    • 2 years ago
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    Hmm, is that 3 in a_11 positive or negative?

  11. iop360
    • 2 years ago
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    this is where im at now\[\left[\begin{matrix}1 & 0 & 0 & 0 & \frac{ -1 }{ 4} & 1 \\ 0 & 1 & 2 & 0 & \frac{ 1 }{ 2 } & \frac{ -3 }{ 2 } \\ 0 & 0 & k & 1 & \frac{ -3 }{ 4 } & 3\end{matrix}\right]\]

  12. iop360
    • 2 years ago
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    postive

  13. iop360
    • 2 years ago
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    how would i express k on the inverse matrix

  14. CliffSedge
    • 2 years ago
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    Continue to reduce it using row operations until you have only the identity matrix on the left.

  15. iop360
    • 2 years ago
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    could i multiplay R3 by 1/k?

  16. iop360
    • 2 years ago
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    multiply*

  17. CliffSedge
    • 2 years ago
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    Looks like you have to.

  18. iop360
    • 2 years ago
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    thanks

  19. CliffSedge
    • 2 years ago
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    The last step ought to be subtracting your new R3 from R2.

  20. CliffSedge
    • 2 years ago
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    *Sorry, twice R3 from R2..

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