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if A=[[1,-2] , [4,5]] and f(t)=t^2-3t+7 ...

if `A=[[1,-2] , [4,5]]` and `f(t)=t^2-3t+7` then `f(A)+[[3,6],[-12,-9]]=`

A

`[(1,0),(0,1)]`

B

`[(0,0),(0,0)]`

C

`[(0,1),(1,0)]`

D

`[(1,1),(0,0)]`

Text Solution

Verified by Experts

The correct Answer is:
B
Now, `A^(2)=[(1,-2),(4,5)][(1,-2),(4,5)]=[(-7,-12),(24,17)]`
Now `f(A)=A^(2)-3A+7`
`=[(-7,-12),(24,17)]-3[(1,-2),(4,5)]+7[(1,0),(0,1)]`
`=[(-7,-12),(24,17)]+[(-3,6),(-12,-15)]+[(7,0),(0,7)]`
`=[(-3,-6),(12,9)]`
`:.f(A)+[(3,6),(-12,-9)]=[(-3,-6),(12,9)]+[(3,6),(-12,-9)]=[(0,0),(0,0)]`
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