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If A=[(1,2),(2,1)] and f(x)=(1+x)/(1-x),...

If `A=[(1,2),(2,1)]` and `f(x)=(1+x)/(1-x)`, then f(A) is

A

`[[1 ,1],[1,1]]`

B

`[[2 ,2],[2,2]]`

C

`[[-1 ,-1],[-1,-1]]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`because f(x) = (1+x)/(1-x)`
`rArr (1-x) f(x) = 1 +x`
`rArr (I-A)f(A) = (I+A)`
` rArr f(A) = (I-A)^(-1) (I+A)`
`([[1,0],[0,1]]-[[1,2],[2,1]])^(-1)([[1,0],[0,1]]+[[1,2],[2,1]])`
`[[0,-2],[-2,0]]^(-1)[[2,2],[2,2]]=-1/4[[0,2],[2,0]][[2,2],[2,2]]`
`=-1/4 [[4,4],[4,4]]=[[-1,-1],[-1,-1]]`
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ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If A=[(1,2),(2,1)] and f(x)=(1+x)/(1-x), then f(A) is

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  2. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

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  3. Evluate int 3x^2 dx

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  4. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  5. If A^(2)-A+I=O, then A^(-1) is equal to

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  6. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

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  7. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  8. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  9. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

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  10. If A and B are square matrices of size nxxn such that A^2-B^2 = (A-B)(...

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  11. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  12. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

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  13. Let A be a square matrix all of whose entries are integers. Then wh...

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  14. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  15. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  16. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  17. The number of 3xx3 matrices A whose are ether 0 or 1 and for which t...

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  18. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  19. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

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  20. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  21. Let p be an odd prime number and T(P) be the following set of 2xx2 m...

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