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Question
Can you explain to me how to solve these matrix equation? These two are throwing me off.

5x - [1.5 -3.6]   [0.2  1.3]
    [-0.3 2.8] = [-5.6 1.7]

-3y + 2[6    9]   [27 -18]
      [-12 15] = [30   6]

Answer
It looks like the equations have 2x2 matrixes, so x and y are also 2x2 matrices.

For the 1st equation, adding
1.5 -3.6
-0.3  2.8
to both sides gives
1.5+0.2  -3.6+1.3
-0.3-5.6   2.9+1.7
on the right side.

The result of this is
1.7 -2.3
-5.9  4.5.

Since this is 5x, dividing by 5 gives
0.34 -0.46
-1.18  0.9.

This is the matrix solution for x.


For y, multiply the matrix by 2 giving
12 18
-24 30.

Subtracting this from both sides gives
15 -36
42  -9.

Since this is -3y, divide the entire matrix by -3 and get
-5 12
-14  3.

This is the y matrix.

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Scott A Wilson

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