Page 122 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

ans =
-3.0000+ 2.0000i 6.0000- 4.0000i
-6.0000+ 4.0000i -9.0000+ 6.0000i

⋅
A
B
Two matrices and are said to be conformable for multiplication A B in that order, only when
the number of columns of matrix is equal to the number of rows of matrix . That is, the prod-
B
A
uct AB⋅ (but not BA⋅ ) is conformable for multiplication only if is an m × p and matrix is
A
B
an p × n matrix. The product AB⋅ will then be an m × n matrix. A convenient way to determine
if two matrices are conformable for multiplication is to write the dimensions of the two matrices
side−by−side as shown below.
Shows that A and B are conformable for multiplication

A B
m × p p × n

Indicates the dimension of the product A ⋅ B

For the product BA⋅ we have:

Here, B and A are not conformable for multiplication

B A
p × n m × p

⋅
For matrix multiplication, the operation is row by column. Thus, to obtain the product AB , we
multiply each element of a row of by the corresponding element of a column of ; then, we
A
B
add these products.

Example 4.3

Given that

1
C = 234 and D = – 1
2
⋅
⋅
compute the products CD and DC
Solution:
The dimensions of matrices and are respectively 1 × 3 3 × 1 ; therefore the product CD⋅ is
C
D
4−4 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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