# MATH 0110 Lecture 3: OPERATIONS BETWEEN MATRICES

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Acadia University

Mathematics and Statistics

MATH 0110

batty

Fall

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OPERATIONS BETWEEN MATRICES
ADD AND SUBTRACT
Two matrices A and B can be added or subtracted only if they have the same size as:
a11 a 12 ... a 1n b11 b12 ... b 1n
a a ... a b b ... b
21 22 2n 21 22 2n
. . . . . . . .
If A B
. . . . . . . .
. . . . . . . .
a m1 am2 ... a mn b m1 b m2 ... b mn
and then:
a b a b ... a b
11 11 12 12 1n 1n
a21 b 21 a 22b 22 ... a 2n b2n
. . . .
A B . . . .
. . . .
a m1 bm1 am2 b m2 ... a mn bmn
MULTIPLICATION BY A SCALE
If
a11 a12 ... a 1n
a 21 a22 ... a 2n
. . . .
A
. . . .
. . . .
a a ... a
m1 m2 mn and c scale , then
ca ca ... ca
11 12 1n
ca21 ca22 ... ca 2n
. . . .
cA . . . .

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