Saturday, May 4, 2013

Verify that A3 – 6A2 + 9A – 4I = O and hence find A–1

Verify that A3 – 6A2+ 9A – 4I = O and hence find A–1
Solution :
Multiply A with A to get A2
 Multiply A2 with A to get A3

We have  A3 – 6A2 + 9A – 4I = O plug the value

Multiply equation by A-1 to get A-1
We get
 A3A-1  – 6A2 A-1  + 9A A-1  – 4I A-1  = O A-1
Solve it we get
A2 – 6A + 9I – 4 A-1= O
A2 – 6A + 9I =4 A-1
or
4 A-1 = A2 – 6A + 9I
Plug the values we get


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