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If A=[(3,1),(7,5)] , find x and y so tha...

If `A=[(3,1),(7,5)]` , find x and y so that `A^2 + xI-yA`=0. Hence find `A^(-1)`

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The correct Answer is:
`x = y = 8 ; 1/8[(5,-1),(-7,3)]`
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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION V)
  1. For what invertile matrix A of order 3 if |A| = 5 then find |adj A|

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  2. Find the adjoint of the following matrices : [(2,-1),(4,3)]

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  3. Find adjoint of the matrix: [[1,2],[3,4]

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  4. Find adjoint of the matrix: [[1,-1,2],[2,3,5],[-2,0,1]]

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  5. If A = [(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)] verify t...

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  6. Verify A(adj A) = (adj A).A = |A|.I :[[2,3],[-4,-6]]

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  7. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

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  8. Find the inverse of the matrix (if it exists): [[-1,5],[-3,2]]

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  9. Using elementary transformations find the inverse of [[1,3,-2],[-3,0,-...

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  10. Find the inverse of the following matrices. [(-1,1,2),(3,-1,1),(-1,3...

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  11. If A = [(2,3),(4,5)] show that A^2-7AI-2 =0 hence find A^(-1)

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  12. If A=[(3,2),(2,1)] verify that A^2-4A-I=0 . Hence find A^(-1)

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  13. If A=[(2,-3),(-4,7)] compute A^(-1) and show that 2A^(-1) + A-9I =0

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  14. If A=[(2,3),(5,-2)] , show that A^(-1)=1/19A

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  15. For what value of x is the matrix [(5-x,x+1),(2,4)] singular ?

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  16. For what value of x is the matrix [(2x+4,4),(x+5,3)] a singular matrix...

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  17. If A=[(3,1),(7,5)] , find x and y so that A^2 + xI-yA=0. Hence find A^...

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  18. Find (AB)^(-1) if A=[(3,4),(1,1)] ,B^(-1)=[(4,3),(2,1)]

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  19. Find (AB)^(-1) if A=[(5,0),(2,3)] ,B^(-1)=[(1,2),(1,4)]

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  20. Find A^(-1) if A=[(0,1,1),(1,0,1),(1,1,0)] and show that A^(-1)=(A^2-3...

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