Question

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

Answer 1

um you gave a list of numbers that in no way resembles a matrix

Answer 2

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

Answer 3

can you reduce it to I?

Answer 4

i think so

Answer 5

i write where i am write now

Answer 6

k brb wife just got home.

Answer 7

this is just the coefficient matrix\[\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 2\\ 0 & 0 & k\end{matrix}\right]\]

Answer 8

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..)

Answer 9

yes i started w/ that

Answer 10

Hmm, is that 3 in a_11 positive or negative?

Answer 11

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

Answer 12

postive

Answer 13

how would i express k on the inverse matrix

Answer 14

Continue to reduce it using row operations until you have only the identity matrix on the left.

Answer 15

could i multiplay R3 by 1/k?

Answer 16

multiply*

Answer 17

Looks like you have to.

Answer 18

thanks

Answer 19

The last step ought to be subtracting your new R3 from R2.

Answer 20

*Sorry, twice R3 from R2..