Expert: Paul Klarreich - 10/3/2006

Question
I'm currently taking Pre-calculus AND DON'T QUITE UNDERSTAND HOW TO SOLVE MATRICES LIKE THIS ONES.....[X 2Y]=[Y+5 X-3]
        [5 4X]=[2X 5Y]
        
        [2X][8-Y]
        [0]=[Y]
        [16][4X]THIS IS A MATRICE OF 3X2

ALSO, HOW TO SOLVE: FIND 2A-3B IF A=[1 7]
                                   [3 2]
AND B=[-4 5]
     [1 -1] HOW CAN YOU DO THIS PROBLEMS? BOTH MATRICES ARE 2X2.  

Answer
Obed Bernal Asks in Category Advanced Math ...
 
Subject:  pRE-cALCULUS
Private:  no
 
Question:  I'm currently taking Pre-calculus AND DON'T QUITE UNDERSTAND HOW TO SOLVE MATRICES LIKE THIS ONES.....
[X 2Y]=[Y+5 X-3]
[5 4X]=[2X 5Y]
       
[2X][8-Y]
[0]=[Y]
[16][4X]THIS IS A MATRICE OF 3X2

ALSO, HOW TO SOLVE: FIND 2A-3B IF A=[1 7]
                                  [3 2]
AND B=[-4 5]
    [1 -1] HOW CAN YOU DO THIS PROBLEMS? BOTH MATRICES ARE 2X2.  

...........................................
Hi, Obed,

I am afraid I can't quite make out the forms you are writing for the first two.  Please resubmit the problems, using a format like this:

[X 2Y] = [Y+5 X-3]
[5 4X] = [2X   5Y]

with everything lined up neatly.  Then I'll know what you are asking.

The last one looks routine.  To do 2A, given a matrix A, just multiply each entry (element) by 2.

2 [ 1  7 ]
 [ 3  2 ]
=
[ 2  14 ]
[ 6   4 ]

And
-3 [ -4  5 ]
  [  1 -1 ]
=
[ 12  -15 ]
[ -3    3 ]

Finally, you can just add those, adding the corresponding elements.  Of course this never works unless the matrices are exactly the same size and shape.

[ 2  14 ]
[ 6   4 ]

Plus

[ 12  -15 ]
[ -3    3 ]

gives

[ 14  - 1 ]
[  3    7 ]
...................................

Regarding the others, it might be that if you are solving a matrix equation, all you have to do is to equate the corresponding elements.

One more thing, if you don't mind.  Please include a subject line that says something about the problem, not one that just names the subject or repeats the category.  In this case, you could write:

Solving Matrix Equations