Page 120 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

*
† The sum of the diagonal elements of a square matrix is called the trace of .
A
A
† A matrix in which every element is zero, is called a zero matrix.
4.2 Matrix Operations

Two matrices A = a ij and B = b ij are equal, that is, A = B , if and only if

,
,
,,,
,
,,
a = b ij i = 1 2 3 … m j = 123 … n (4.2)
ij
Two matrices are said to be conformable for addition (subtraction), if they are of the same order
m × . n
If A = a ij and B = b ij are conformable for addition (subtraction), their sum (difference) will
be another matrix with the same order as and , where each element of is the sum (dif-
B
C
C
A
ference) of the corresponding elements of and , that is,
B
A
C = A ± B = [ a ± b ] ij (4.3)
ij
Example 4.1

Compute A + B and A – B given that

A = 123 and B = 23 0
01 4 – 1 25
Solution:

A + B = 1 + 2 2 + 3 3 + 0 = 35 3
0 – 1 1 + 2 4 + 5 – 1 3 9
and

–
–
–
A – B = 12 2 – 3 30 = – 1 1 3
–
0 + 1 1 – 2 4 – 5 1 – 1 1
Check with MATLAB:

A=[1 2 3; 0 1 4]; B=[2 3 0; −1 2 5]; % Define matrices A and B
A+B % Add A and B

* Henceforth, all paragraphs and topics preceded by a dagger ( † ) may be skipped. These are discussed in matrix theory text-
books.

4−2 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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