Page 121 - Numerical Analysis Using MATLAB and Excel

Matrix Operations

ans =
3 5 3
-1 3 9

A−B % Subtract B from A
ans =
-1 -1 3
1 -1 -1

If is any scalar (a positive or negative number), and not [ ] which is a 1 × 1 matrix, then mul-
k
k
tiplication of a matrix by the scalar , is the multiplication of every element of by . k
k
A
A
Example 4.2
Multiply the matrix

–
A = 12
23

by (a) k = 5 and (b) k = – 3 + j2
1
2
Solution:
a.

–
k ⋅ A = 5 × 12 = 5 × 1 5 × – ( 2 ) = 5 – 10
1
23 5 × 2 5 × 3 10 15

b.
)
)
–
k ⋅ A = – ( 3 + j2 × 12 = – ( 3 + j2 × 1 ( – 3 + j2 × – ( 2 ) = – 3 + j2 6 – j4
)
2
)
)
23 – ( 3 + j2 × 2 – ( 3 + j2 × 3 – 6 + j4 – 9 + j6
Check with MATLAB:
k1=5; k2=(−3 + 2*j); % Define scalars k and k
1 2
A=[1 −2; 2 3]; % Define matrix A
k1*A % Multiply matrix A by constant k
1
ans =
5 -10
10 15
k2*A %Multiply matrix A by constant k
2

Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−3
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