5s 15t 4 0 8 3 the region for our parameters s and t

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Unformatted text preview: n two matrices of the same size, the matrix obtained by adding the corresponding entries of the two matrices is called the sum of the two matrices. More specifically, if A = [aij ]m×n and B = [bij ]m×n , we define A + B = [aij ]m×n + [bij ]m×n = [aij + bij ]m×n As an example, consider the sum below. 1 Recall that means A has m rows and n columns. Critics may well ask: Why not leave it at that? Why the need for all the notation in Definition 8.6? It is the authors’ attempt to expose you to the wonderful world of mathematical precision. 2 8.3 Matrix Arithmetic 477 2 3 −1 4 2 + (−1) 3+4 1 7 4 −1 + −5 −3 = 4 + (−5) (−1) + (−3) = −1 −4 0 −7 8 1 0+8 (−7) + 1 8 −6 It is worth the reader’s time to think what would have happened had we reversed the order of the summands above. As we would expect, we arrive at the same answer. In general, A + B = B + A for matrices A and B , provided they are the same size so that the sum is defined in the first place. This is the commutative law of matrix addition. To see why this is true in general, we appeal to the definition of matrix addition. Given A = [aij ]m×n and B = [bij ]m×n...
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