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Question 1127893: Equality of Matrices. Solve for x and y.
[x 2y] = [2 -2]
[4 6] [2x -6y]
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Answers: x = 2, y = -1
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To get these answers, you simply equate the corresponding pieces of the two matrices.
The top left corner of the left and right matrices are x and 2 respectively. Those entries must be the same for the entire two matrices overall to be equal. Therefore, x = 2.
Through similar reasoning, the top right corners must also be equal, so 2y = -2 leads to y = -1
As a check, note how the bottom left corners are 4 and 2x. So 4 = 2x which solves to x = 2, confirming our prior solution above.
Finally, the bottom right corners equate to get 6 = -6y and solve to get y = -1. This backs up the other solution.
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