953 9.7 Properties of Matrices CHECK Confirm that A + 1-A2 equals the zero matrix, O. A + 1-A2 = c -5 3 2 4 -1 -6d + c 5 -3 -2 -4 1 6d = c 0 0 0 0 0 0d = O ✓ Matrix -A is the additive inverse, or negative, of matrix A. Every matrix has an additive inverse. Matrix Subtraction The real number b is subtracted from the real number a, written a - b, by adding a and the additive inverse of b. a - b = a + 1-b2 Real number subtraction The same definition applies to subtraction of matrices. Subtraction of Matrices If A and B are two matrices of the same dimension, then the following holds true. A −B =A + 1 −B2 In practice, the difference of two matrices of the same dimension is found by subtracting corresponding elements. EXAMPLE 3 Subtracting Matrices Find each difference, if possible. (a) c -5 2 6 4d - c -3 5 2 -8d (b) 38 6 -44 - 33 5 -84 (c) A - B, if A = c -2 0 5 1d and B = c 3 5d SOLUTION (a) c -5 2 6 4d - c -3 5 2 -8d = c -5 - 1-32 2 - 5 6 - 2 4 - 1-82 d Subtract corresponding entries. = c -2 -3 4 12d Simplify. (b) 38 6 -44 - 33 5 -84 = 35 1 44 Subtract corresponding entries. (c) A = c -2 0 5 1d and B = c 3 5d These matrices have different dimensions and cannot be subtracted, so the difference A - B does not exist. S Now Try Exercises 31, 33, and 35. This screen supports the result in Example 3(a).
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