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# 2-17 - Problem 2-17 Given the following 33 matrices i-3 5-4...

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Problem 2-17 Given the following 3 ä 3 matrices A = i k j j j j j j j - 3 5 - 4 6 1 9 4 - 3 2 y { z z z z z z z B = i k j j j j j j j 2 - 1 3 1 2 5 - 3 - 5 2 y { z z z z z z z determine A+B and A-3B Solution If A ij is the element in the i th row and j th column of A , and B ij is the element in the i th row and j th column of B , then A+B is A ij + B ij Thus A + B= i k j j j j j j j - 3 + 2 5 - 1 - 4 + 3 6 + 1 1 + 2 9 + 5 4 - 3 - 3 - 5 2 + 2 y { z z z z z z z = i k j j j j j j j - 1 4 - 1 7 3 14 1 - 8 4 y { z z z z z z z Multiplication of a matrix A with a scalar a means every element in A is multiplied by the scalar. Thus (1) a A = a i k j j j j j j j - 3 5 - 4 6 1 9 4 - 3 2 y { z z z z z z z = i k j j j j j j j - 3 a 5 a - 4 a 6 a 1 a 9 a 4 a - 3 a 2 a y { z z z z z z z Thus
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