508 Chapter 18Matrices and linear transformations
EXAMPLES 18.8Matrix multiplication
(i) Two square matrices:
(ii) Two rectangular matrices:
(iii) Row vector 1 × 1 column vector:
(iv) Column vector 1 × 1 row vector:
(v) Matrix 1 × 1 column vector:
(vi) Row vector 1 × 1 matrix:
0 Exercises 21–37
() ( )123
20 3
11 2
12 0
18 7
−
−
−
=−
20 3
11 2
1
2
3
7
3
−
−
=
−
−
2
2
1
123
246
246
123
−
=− − −
()
()()123
2
2
1
− 11
==
20 3
11 2
2341
1220
0120
− 4
−
−
=
9922
3721
23 3
dimensions: () (4×× 424)() ×
cd
cd
ab
ab
c
1
1221
1221=
aada cbdb
ca da cb db
112
11 1221 22 21 22++
++