959 9.7 Properties of Matrices (c) The total cost of all the materials is given by the product of matrix T, the total amounts matrix, and matrix R, the cost matrix. To multiply these matrices and obtain a 1 * 1 matrix, representing the total cost, requires multiplying a 1 * 4 matrix and a 4 * 1 matrix. This is why in part (b) a row matrix was written rather than a column matrix. The total materials cost is given by TR, so TR = 33800 130 1400 2004≥ 20 180 60 25¥ = 3188,4004. The total cost of materials is $188,400. This total may also be found by summing the elements of the column matrix 1PQ2R. S Now Try Exercise 85. 9.7 Exercises CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. 1. For the following statement to be true, the value of x must be , and the value of y must be . c 3 -6 5 1d = c x + 1 -6 5 y + 1d 2. For the following sum to be true, we must have w = , x = , y = , and z = . c 0 5 -3 10d + c 1 2 3 4d = c w x y zd 3. For the following difference to be true, we must have w = , x = , y = , and z = . c 7 2 5 12d - c 1 3 6 0d = c w x y zd 4. For the following scalar product to be true, we must have w = , x = , y = , and z = . -2 c 5 -1 6 0d = c w x y zd 5. If the dimension of matrix A is 3 * 2 and the dimension of matrix B is 2 * 6, then the dimension of AB is . 6. For the following matrix product to be true, we must have x = . c 2 1 -4 3d c 3 -1 2 7d = c x 5 -6 25d Concept Check Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1. 8. c -9 4 6 1 2 8d 9. £ -6 4 3 8 1 -5 0 9 7 0 2 1§ 7. c -4 2 8 3d 10. 38 -2 4 6 34 11. c 2 4d 12. 3-94
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