If and then
If then
If then
Finally, we present the MATLAB approach to obtain the inverse of a square matrix.
If all elements of the matrix are given as numerical values, this approach is best.
MATLAB Approach to Obtain the Inverse of a Square Matrix. The inverse of
a square matrix Acan be obtained with the command
inv(A)
For example, if matrix Ais given by
then the inverse of matrix Ais obtained as follows:
A= C
112
340
125
S
c
AB
CD
d
- 1
= c
T-^1 - T-^1 BD-^1
- D-^1 CT-^1 D-^1 +D-^1 CT-^1 BD-^1
d
@D@ Z0,T=A-BD-^1 C, and @T@ Z0,
c
AB
CD
d
- 1
= c
A-^1 +A-^1 BS-^1 CA-^1 - A-^1 BS-^1
- S-^1 CA-^1 S-^1
d
@A@ Z0,S=D-CA-^1 B,@S@ Z0,
c
A0
CD
d
- 1
= c
A-^10
- D-^1 CA-^1 D-^1
d
c
AB
0D
d
- 1
= c
A-^1 - A-^1 BD-^1
0D-^1
d
@A@ Z 0 @D@Z0,
Appendix C / Vector-Matrix Algebra 879