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If A=[(2,3),(1,-2)] and A^(-1)=alphaA, t...

If `A=[(2,3),(1,-2)]` and `A^(-1)=alphaA,` then `alpha` is equal to

A

7

B

`-7`

C

`(1)/(7)`

D

`-(1)/(7)`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-MATRICES-CRITICAL THINKING ( 2. 1 Elementary Transformations)
  1. If A is a singular matrix, then adj A is a. singular b. non singula...

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  2. If A is a singular matrix of order n, then A(adjA)=

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  3. If A=[(a,b),(c,d)], then adj(adjA) is equal to

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  4. Using elementary transformations, find the inverse of the matrix : ...

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  5. The inverse of the matrix A[(1,1,1),(6,7,8),(6,7,-8)] using adjoint me...

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  6. If D=diag [2, 3, 4], then D^(-1)=

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  7. The matrix A satisfying A[[1, 5], [0, 1]]=[[3, -1], [6, 0]] is

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  8. If product of matrix A with [(1,1),(2,0)] is [(3,2),(1,1)] then A^(-1)...

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  9. If product of matrix A with [(0,1),(2,-4)] is [(3,2),(1,1)] , then A^(...

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  10. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

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  11. If the product of the matrix B=[(2,6,4),(1,0,1),(-1,1,-1)] with a m...

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  12. If P=[(1,2,4),(3,1,0),(0,0,1)], Q=[(1,-2,-3),(-3,1,9),(0,0,-5)]then (P...

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  13. If A=[(2,3),(1,-2)] and A^(-1)=alphaA, then alpha is equal to

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  14. If matrix [(1,2,-1),(3,4,5),(2,6,7)] and its inverse is denoted by A^(...

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  15. Show that A=[(5,3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus, ...

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  16. If [(x,1),(1,0)] and A^(2)=I, then A^(-1) is equal to

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  17. If A and B are square matrices of the same order and AB=3I then A^(-1)...

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  18. A square non-singular matrix A satisfies A^2-A+2I=0," then "A^(-1)=

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  19. If A is a square matrix such that |A| ne 0 and m, n (ne 0) are scalars...

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  20. If a matrix A is such that 4A^(3)+2A^(2)+7A+I=0, then A^(-1) equals

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