# Thread: Solving for a solution variable in a matrix

1. ## 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!

2. ## Re: Solving for a solution variable in a matrix

Hello, dwnicke!

$\displaystyle \text{The example we are given in the book is as follows: }\:\begin{bmatrix}1&2&\text{-}1 \\ \text{-}6 & \text{-}5 & 2 \\ 5 & \text{-}18 & h \end{bmatrix}$

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:

. . $\displaystyle \begin{Bmatrix} x + 2y &=& \text{-}1 \\ \text{-}6x - 5y &=& 2 \\ 5x - 18y &=& h \end{Bmatrix}$

And the question is: "What value of $\displaystyle h$ will make the system consistent?"

The answer is: .$\displaystyle h = 11.$

3. ## 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.

4. ## 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.