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Question

If X and Y are 2×2 matrices, then solve the following matrix equations for X and Y.
2X+3Y=[2340],3X+2Y=[2215]

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Solution

2X+3Y=[2340] ........(1)
3X+2Y=[2215] ........(2)
3×(1)2×(2)

6X+9Y=[69120]

6X+4Y=[44410]

6X+9Y6X4Y=[6+4941240+10]

5Y=[105810]

Y=21852

We have from (1)

2X+3Y=[2340]

2X=[2340]3Y

2X=[2340]321852

2X=[2340]632456

2X=2633424506

2X=40202456

2X=40456

X=20253


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