972 CHAPTER 9 Systems and Matrices (b) The coefficient matrix A for this system is A = £ 1 2 3 0 -2 0 1 -1 0§, and its inverse A-1 was found in Example 2. Let X = £ x y z§ and B = £ -1 5 6§. Because X = A-1B, we have £x y z§ = D 0 - 1 2 1 0 - 1 2 0 1 3 1 2 - 1 3T£ -1 5 6§ (11111111)11111111* A-1 from Example 2 = £ 2 1 -3§. The solution set is 512, 1, -326. (b) Figure 31 shows the coefficient matrix 3A4 and the column matrix of constants 3B4. Be sure to enter the product of 3A4-1 and 3B4 in the correct order. Remember that matrix multiplication is not commutative. Figure 31 S Now Try Exercises 35 and 49. 9.8 Exercises CONCEPT PREVIEW Answer each question. 1. What is the product of c 6 4 -1 8d and I2 (in either order)? 2. What is the product £ -5 7 4 2 3 0 -1 6 6§ £ 1 0 0 0 1 0 0 0 1§? 3. It can be shown that the following matrices are inverses. What is their product (in either order)? c 5 1 4 1d and c 1 -1 -4 5R 4. It can be shown that the following matrices are inverses. What is their product (in either order)? £ 1 0 0 0 -1 0 -1 0 1§ and £ 1 0 0 0 -1 0 1 0 1§ 5. What is the coefficient matrix of the following system? 3x - 6y = 8 -x + 3y = 4
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