Page 140 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

α 11 α 21 α 31 …α n1

α 12 α 22 α 32 …α n2
adjA = α 13 α 23 α 33 …α n3 (4.41)
…… … … …
α 1n α 2n α 3n …α nn

We observe that the cofactors of the elements of the ith row (column) of , are the elements of
A
the ith column (row) of adjA .

Example 4.12
Compute adjA given that

1 2 3
A = 1 3 4 (4.42)
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Solution:

3 4 – 2 3 2 3
4 3 4 3 34
– 7 6 – 1
adjA = – 1 4 1 3 – 2 3 = 10 – 1
1 3 1 3 3 4
–
12 1
1 3 – 12 12
1 4 14 13

4.9 Singular and Non−Singular Matrices

An square matrix is called singular if detA = 0 ; if detA ≠ , 0 A is called non−singular. If an n
n
A
square matrix is nearly singular, that is, if the determinant of that matrix is very small, the
A
matrix is said to be ill−conditioned. This topic is discussed in Appendix C.

Example 4.13
Given that

4−22 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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