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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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