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If A=[3 1-1 2] , show that A^2-5A+7I=O ....

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:
`(1)/(7)[{:(2,-1),(1,3):}]`
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MODERN PUBLICATION-DETERMINANTS-Exercise 4(g) (SHORT ANSWER TYPE QUESTIONS)
  1. Verify A(adj.A)=(adj.A)A=|A|I: [{:(2,3),(-4,-6):}]

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

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  3. Verify that A(adjA)=I when : A=[{:(cos theta, -sintheta,0),(sintheta,...

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  4. Find the inverse of each of the following matrice : [{:(-1,5),(-3,2)...

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  5. Find the inverse of each of the following matrice : [{:(2,-2),(4,3):...

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  6. If A=[{:(2,-1),(-1,2):}], verify A^(2)-4A+3I=0, where I=[{:(1,0),(0,1)...

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

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  8. Consider the matrix A=[{:(2,3),(4,5):}]. Show that A^(2)-7A-2I=O

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  9. Consider the matrix A=[{:(2,3),(4,5):}]. Hence , find A^(-1).

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  10. If A=[{:(2,3),(5,-2):}], write A^(-1) in terms of A.

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  11. Verify (AB)^(-1)=B^(-1)A^(-1) for the matrices A and B where A=[{:(2...

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  12. Verify (AB)^(-1)=B^(-1)A^(-1) for the matrices A and B where A=[{:(3...

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  13. Verify (AB)^(-1)=B^(-1)A^(-1) for the matrices A and B where A=[{:(3...

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  14. Verify (AB)^(-1)=B^(-1)A^(-1) for the matrices A and B where A=[{:(4...

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  15. Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^(2)-...

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

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

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  18. For the matrix A=[{:(2,1),(3,0):}] , find the numbers 'a' and 'b' such...

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  19. If A=[{:(2,-3),(-4,7):}], compute A^(-1) and show that 2A^(-1)+A-9I=O.

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