s
Section 5.7 Matrices
449
addition of two matrices a and b is defined only when a and b have the
same dimensions; then it is simply a matter of adding the corresponding elements.
Formally, if a and b are both n × m matrices, then C = a + b is an n × m
matrix with entries
c ij = a ij + b ij
PRaCtiCe 51 For r = 2,
a = £
1 7
−3 4
5 6
§
b = £
4 0
9 2
−1 4
§
find ra + b.
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subtraction of matrices is defined by a − b = a + (−l)b.
In a zero matrix, all entries are 0. If we add an n × m zero matrix, denoted
by 0, to any n × m matrix a, the result is matrix a. We can symbolize this by the
matrix equation
0 + a = a
This equation is true because of a similar equation that holds for all the individual
numerical entries, 0 + a ij = a ij . Other matrix equations are also true because of
similar equations that hold for the individual entries.
example 67
For
a = £
1 3 6
2 0 4
−4 5 1
§
b = £
0 −2 8
1
5 2
2
3 3
§
the matrix a + b is
a + b = £
1 1 14
3 5
6
−2 8
4
§