# Solving a Matrix with variables

1. Jan 16, 2013

### brownman

1. The problem statement, all variables and given/known data

Find all values of k, if any, that satisfy the equation.

[2 2 k]*[1 3 0; 3 0 5; 0 5 -1][2 ; 2 ; k]=0

2. Relevant equations

3. The attempt at a solution

Multiplying the two matrices on the right

[2 2 k] * [8 ; 6 +5k ; 10-k]=0

Multiply again

[ 16 + 10+12k + 10k-k^2]=0

I'm stuck here, because I'm really confused about whether this is a homogeneous matrix or not, or if there are infinite solutions to k because the variable just needs to be zero.

Thanks for any help :)

2. Jan 16, 2013

### Staff: Mentor

I'm not sure I understand your notation, but it looks for the matrix product to be zero, you need 16 + 10+12k + 10k-k^2 = 0. That's a quadratic equation, so should be easy to solve for k.

3. Jan 16, 2013

### brownman

I've left it in matlab notation, so the semi colons indicate a new row and spaces mean the next entry is in the next column.

Thanks for helping me clear that up, I used the quadratic equation to solve for k but I got the roots 10±8$\sqrt{2}$ which are apparently incorrect. Perhaps it's at this point an error with my online homework system. Oh well.

4. Jan 17, 2013

### Staff: Mentor

You transposed a couple of numbers. It should be 16 + 12 + 10k + 10k - k^2 = 0
This part is irrelevant - the exercise is to find values of k for which the matrix product is 0.

5. Jan 17, 2013

### brownman

I believe I made a typo here in entering, as I still return $10\pm8\sqrt{2}$ as the roots. The problem has been solved though, my instructor sent an email regarding the error with the homework system.

Again, thank you for your help!