# A simple matrix help

• March 1st 2010, 04:49 AM
llkkjj24
A simple matrix help
Hi . can anyone tell me the steps to do a matrix like this, its a bit confusing.

Given That : top: a + b 2a-8
bottom: a - b 0

= top 7 2
bottom 3 0

find a and b

sorry for not using latex but the code is a bit complicated...
they are all 2 * 2 matrix with a + b , 2a-8 on top for the first matrix
a-b , 0 in the bottom of the first matrix

and the second matrix is 7 , 2 on top and 3, 0 in the bottom

they are seperated by a equals sign

they question is to find a and b
• March 1st 2010, 05:56 AM
HallsofIvy
Quote:

Originally Posted by llkkjj24
Hi . can anyone tell me the steps to do a matrix like this, its a bit confusing.

Given That : top: a + b 2a-8
bottom: a - b 0

= top 7 2
bottom 3 0

find a and b

sorry for not using latex but the code is a bit complicated...
they are all 2 * 2 matrix with a + b , 2a-8 on top for the first matrix
a-b , 0 in the bottom of the first matrix

and the second matrix is 7 , 2 on top and 3, 0 in the bottom

they are seperated by a equals sign

they question is to find a and b

So
$\begin{bmatrix}a+ b & 2a- 8 \\ a- b & 0\end{bmatrix}= \begin{bmatrix}7 & 2 \\ 3 & 0\end{bmatrix}$
(click on that to see the LaTex code I used.)

Since equality for matrices is defined to mean that all corresponding entries are equal, that tells you that a+ b= 7, 2a- 8= 2, a- b= 3, and 0= 0. Since that is three equations ("0= 0" is always true, of course) for two unknown values, it may be "over determined", that is, there may not be 2 numbers that satisfy all three equations.

I recommend starting by adding the first and third equations. That will immediately eliminate b and you can solve for a. The use any one of the equation to find the value of b for that a. Finally, check that all equations are satified.