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Unformatted text preview: he additive inverse of a matrix,
3 A technical detail which is sadly lost on most readers. 478 Systems of Equations and Matrices take additive inverses of each of its entries. With the concept of additive inverse well in hand, we
may now discuss what is meant by subtracting matrices. You may remember from arithmetic that
a − b = a + (−b); that is, subtraction is deﬁned as ‘adding the opposite (inverse).’ We extend this
concept to matrices. For two matrices A and B of the same size, we deﬁne A − B = A + (−B ). At
the level of entries, this amounts to
A − B = A + (−B ) = [aij ]m×n + [−bij ]m×n = [aij + (−bij )]m×n = [aij − bij ]m×n
Thus to subtract two matrices of equal size, we subtract their corresponding entries. Surprised?
Our next task is to deﬁne what it means to multiply a matrix by a real number. Thinking back to
arithmetic, you may recall that multiplication, at least by a natural number, can be thought of as
‘rapid addition.’ For example, 2 + 2 +...
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