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If A=[{:(3,1),(-1,2):}] show that A^2-5A...

If `A=[{:(3,1),(-1,2):}]` show that `A^2-5A+7I=O`. Hence find `A^(-1)`

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The correct Answer is:
`thereforeA^(-1)=1/7[{:(2,-1),(1,3):}]`
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KUMAR PRAKASHAN-DETERMINANTS -Exercise 4.5
  1. Find adjoint of each of the matrices in Exercises 1 and 2 [{:(1,2),(...

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  2. Find adjoint of each of the matrices in Exercises 1 and 2 [{:(1,-1,2...

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  3. Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:(...

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  4. Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:...

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  5. Find the inverse of each of the matrices (if it exists ) {:[( 2,-2),...

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  6. Find the inverse of each of the matrices (if it exists ) {:[( 2,-2),...

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  7. Find the inverse of each of the following matrices (if it exits) given...

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  8. Find the inverse of each of the following matrices (if it exits) given...

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  9. Find the inverse of each of the following matrices (if it exits) given...

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  10. Find the inverse of each of the following matrices (if it exits) given...

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  11. Find the inverse of each of the following matrices (if it exits) given...

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  12. Let A=[{:(3,7),(2,5):}] and B=[{:(6,8),(7,9):}] Verify that (AB)^(-1)=...

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  13. If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O. Hence find A^(-1)

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  14. For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such tha...

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  15. For the matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] Show that A^3-6A^2+5A...

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  16. If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] Verify the result A^3-6A^2+9A-4...

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  17. Let A be a nonsingular square matrix of order 3xx3.Then |adj A| is equ...

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  18. If A is an invertible matrix of order 2, then det (A^(-1)) is equal to...

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