Saturday, May 4, 2013

For the matrix A=find the numbers a and b such that A2 + aA + bI = O.

For the matrix A=find the numbers a and b such that A2 + aA + bI = O. 
Answer :


Plug the values in A2 + aA + bI = O 
Solve it we get
                 … (1)

Equate the corresponding element we get
4+a = 0
a = - 4
and
3+a+b = 0
Plug the value of a = - 4 we get
3- 4+ b = 0
b = 1
plug the value in equation 1 we get
  
hence a = -4 and b = 1 satisfied the condition
We have A2 + aA + bI = O
Plug the value of a and b
A2 - 4A + I = O
Multiply by A-1  we get
A2 A-1- 4A A-1+ I A-1 = O A-1
A – 4I +A-1 =  O
A-1 = 4I – A
Plug the value we get


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