Thread: 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!

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: .

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.

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