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The Inverse of a Matrix

1 2 3
A = 2 3 4 (4.43)
3 5 7

determine whether this matrix is singular or non−singular.

Solution:

1 2 3 12
detA = 2 3 4 23 = 21 + 24 + 30 – 27 – 20 28 = 0
–
3 5 7 35

Therefore, matrix is singular.
A

4.10 The Inverse of a Matrix

n
A
B
If and B are square matrices such that AB = BA = I , where is the identity matrix, is
I
called the inverse of , denoted as B = A 1 – , and likewise, is called the inverse of , that is,
A
A
B
A = B 1 –
If a matrix is non−singular, we can compute its inverse from the relation
A
1
A 1 – = ------------adjA (4.44)
detA

Example 4.14
Given that

1 2 3
A = 1 3 4 (4.45)
143

compute its inverse, that is, find A 1 –
Solution:

Here, detA = 9 ++ 12 9 16 – 6 = – 2 , and since this is a non−zero value, it is possible to
8
–
–
compute the inverse of using (4.44).
A
From Example 4.12,

Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−23
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