952 CHAPTER 9 Systems and Matrices EXAMPLE 2 Adding Matrices Find each sum, if possible. (a) c 5 8 -6 9d + c -4 8 6 -3d (b) £ 2 5 8§ + £ -6 3 12§ (c) A + B, if A = c 5 6 8 2d and B = c 3 4 9 2 1 5d ALGEBRAIC SOLUTION (a) c 5 8 -6 9d + c -4 8 6 -3d = c 5 + 1-42 8 + 8 -6 + 6 9 + 1-32 d = c 1 16 0 6d (b) £ 2 5 8§ + £ -6 3 12§ = £ -4 8 20§ (c) The matrices A = c 5 6 8 2d and B = c 3 4 9 2 1 5d have different dimensions, so A and B cannot be added. The sum A + B does not exist. GRAPHING CALCULATOR SOLUTION (a) Figure 25 shows the sum of matrices A and B. Figure 25 (b) The screen in Figure 26 shows how the sum of two column matrices entered directly on the home screen is displayed. Figure 27 Figure 26 (c) A graphing calculator such as the TI-84 Plus will return an ERROR message if it is directed to perform an operation on matrices that is not possible due to dimension mismatch. See Figure 27. S Now Try Exercises 25, 27, and 29. Special Matrices A matrix containing only zero elements is a zero matrix. A zero matrix can be written with any dimension. O= 30 0 04 1 * 3 zero matrix O= c 0 0 0 0 0 0d 2 * 3 zero matrix By the additive inverse property, each real number has an additive inverse: If a is a real number, then there is a real number -a such that a + 1-a2 = 0 and -a + a = 0. Given matrix A, there is a matrix -A such that A + 1-A2 = O. The matrix -A has as elements the additive inverses of the elements of A. (Remember, each element of A is a real number and therefore has an additive inverse.) Example: If A = c -5 3 2 4 -1 -6d , then -A = c 5 -3 -2 -4 1 6d .
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