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If A is non-singular and (A-2I)(A-4I)=0 ...

If `A` is non-singular and `(A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1)` is equal to a.`0I ` b. `2I` c. `6I` d. `I`

A

I

B

O

C

2I

D

6I

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`(A-2I)(A-4I)=O`
`rArr A^2-2A-4A+8I=O`
`rArr A^2-6A+8I=O`
`rArr A^(-1) (A^2-6A+8I)=A^9-1)O`
`rArr A-6I+8A^(-1)=O`
`rArr A+8A^(-1)=6IrArr 1/6A +4/3A^(-1)=I`
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Section I - Solved Mcqs
  1. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

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  2. if A=[{:(0,1,-1),(2,1,3),(3,2,1):}]then (A(adjA)A^-1)A is equal to

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  3. If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equa...

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  4. If A is an invertible matrix of order 3xx3 such that |A|=2 . Then, ...

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  5. If A and B are squre 3xx3 such that A is an orthogonal matrix and B is...

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  6. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

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  7. about to only mathematics

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  8. If A=[(1,0,0),(0,1,1),(0,-2,4)] , 6A^(-1)=A^2+cA+dI, then (c,d) is :

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

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  10. If U={:[(1,2,2),(-2,-1,-1),(1,-4,-3)]:}' ,sum of elements of inverse o...

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  11. If U is same as in Example 50, then the value of {:[(3,2,0)]U[(3),(2),...

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

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  13. If A and B are any two different square matrices of order n with A^3=B...

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  14. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

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  15. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

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

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  17. If {:A=alpha[(1,1+i),(1-i,-1)]:}a in R, is a unitary matrix then alpha...

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  18. The value of a,b,c when [(0,2b,c),(a,b,-c),(a,-b,c)] is orthogonal , ...

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  19. If A=[a(ij)](nxxn), where a(ij)=i^100+j^100, then lim(ntooo) ((overse...

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  20. If A and B are two non-singular matrices which commute, then (A(A+B)^...

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