## iop360 Group Title 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 one year ago one year ago

1. zzr0ck3r Group Title

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

2. iop360 Group Title

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

3. zzr0ck3r Group Title

can you reduce it to I?

4. iop360 Group Title

i think so

5. iop360 Group Title

i write where i am write now

6. zzr0ck3r Group Title

k brb wife just got home.

7. iop360 Group Title

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

8. CliffSedge Group Title

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 Group Title

yes i started w/ that

10. CliffSedge Group Title

Hmm, is that 3 in a_11 positive or negative?

11. iop360 Group Title

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 Group Title

postive

13. iop360 Group Title

how would i express k on the inverse matrix

14. CliffSedge Group Title

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

15. iop360 Group Title

could i multiplay R3 by 1/k?

16. iop360 Group Title

multiply*

17. CliffSedge Group Title

Looks like you have to.

18. iop360 Group Title

thanks

19. CliffSedge Group Title

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

20. CliffSedge Group Title

*Sorry, twice R3 from R2..