anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zzr0ck3r
  • zzr0ck3r
um you gave a list of numbers that in no way resembles a matrix
anonymous
  • anonymous
\[\left[\begin{matrix}3 & 0 & k \\ 12 & 8 & 16\\ 4 & 2 & 4\end{matrix}\right]^{-1}\]
zzr0ck3r
  • zzr0ck3r
can you reduce it to I?

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anonymous
  • anonymous
i think so
anonymous
  • anonymous
i write where i am write now
zzr0ck3r
  • zzr0ck3r
k brb wife just got home.
anonymous
  • anonymous
this is just the coefficient matrix\[\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 2\\ 0 & 0 & k\end{matrix}\right]\]
anonymous
  • anonymous
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..)
anonymous
  • anonymous
yes i started w/ that
anonymous
  • anonymous
Hmm, is that 3 in a_11 positive or negative?
anonymous
  • anonymous
this is where im at now\[\left[\begin{matrix}1 & 0 & 0 & 0 & \frac{ -1 }{ 4} & 1 \\ 0 & 1 & 2 & 0 & \frac{ 1 }{ 2 } & \frac{ -3 }{ 2 } \\ 0 & 0 & k & 1 & \frac{ -3 }{ 4 } & 3\end{matrix}\right]\]
anonymous
  • anonymous
postive
anonymous
  • anonymous
how would i express k on the inverse matrix
anonymous
  • anonymous
Continue to reduce it using row operations until you have only the identity matrix on the left.
anonymous
  • anonymous
could i multiplay R3 by 1/k?
anonymous
  • anonymous
multiply*
anonymous
  • anonymous
Looks like you have to.
anonymous
  • anonymous
thanks
anonymous
  • anonymous
The last step ought to be subtracting your new R3 from R2.
anonymous
  • anonymous
*Sorry, twice R3 from R2..

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