Page 142 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

– 7 6 – 1
adjA = 10 – 1
1 – 2 1
Then,

–
– 7 6 – 1 3.5 3 0.5
1
1
A 1 – = ------------adjA = ------ 10 – 1 = – 0.5 00.5 (4.46)
detA – 2
–
1 – 2 1 – 0.5 10.5
Check with MATLAB:

A=[1 2 3; 1 3 4; 1 4 3], invA=inv(A) % Define matrix A and compute its inverse
A =
1 2 3
1 3 4
1 4 3
invA =
3.5000 -3.0000 0.5000
-0.5000 0 0.5000
-0.5000 1.0000 -0.5000

I
A
Multiplication of a matrix by its inverse A 1 – produces the identity matrix , that is,
1 –
AA 1 – = I or A A = I (4.47)

Example 4.15

Prove the validity of (4.47) for

A = 4 3
2 2
Proof:
–
detA = 8 – 6 = 2 and adjA = 23
– 2 4
Then,
⁄
1
--
-
A 1 – = ------------adjA = 1 2 – 3 = 1 – 3 2
detA 2 – 2 4 – 1 2
and

4−24 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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