Definition. Two matrices A and B are said to be equal, written A = B, if they are of the same order and if all corresponding entries are equal.

For example,



but

[2   -2]

Example. Given the matrix equation



find x and y.

Solution. By the definition of equality of matrices,

x + y = 1
x - y =  3

Solving gives x = 2 and y = -1.

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