Solving for a solution variable in a matrix

The example we are given in the book is as follows:

__a1__ __a2__ __b__

1 2 -1

-6 -5 2

5 -18 h

I'm assuming we put the matrix into row echelon form...making the bottom row "0 0 h" and solve for h. However, when I get to the point of calculating "-18" to "0" ... I'm having a little trouble. Can someone help me get past this final step. Thank you!

Re: Solving for a solution variable in a matrix

Hello, dwnicke!

Can you give us the original wording of the problem?

We don't know what to "do" with that matrix.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I just had a wild idea . . . bear with me.

Suppose that matrix came from a system of equations:

. .

And the question is: "What value of will make the system consistent?"

The answer is: .

Re: Solving for a solution variable in a matrix

The question being asked is: For what value(s) of h is **b** in the plane spanned by a1 and a2?

Thank you for your help. Also, how did you get that awesome text to display matrix!?! I couldn't find it anywhere.

Re: Solving for a solution variable in a matrix

Soroban, I worked it out similarly to what you have done and got the same answer. Thank you again for your help.