# Solving for a solution variable in a matrix

• Sep 20th 2012, 03:38 PM
dwnicke
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!
• Sep 20th 2012, 04:59 PM
Soroban
Re: Solving for a solution variable in a matrix
Hello, dwnicke!

Quote:

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

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:

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

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

The answer is: . $h = 11.$
• Sep 20th 2012, 05:14 PM
dwnicke
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.
• Sep 20th 2012, 06:10 PM
dwnicke
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.