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For the matrix A=[1 1 1 1 2-3 2-1 3] . S...

For the matrix `A=[1 1 1 1 2-3 2-1 3]` . Show that `A^3-6A^2+5A+11\ I_3=O` . Hence, find `A^(-1)` .

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The correct Answer is:
`A^(-1) =(1)/(11) {:[( -3,4,5),(9,-1,-4),(5,-3,-1)]:}`
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For the matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] Show that A^3-6A^2+5A+11I=O . Hence find A^(-1)

For matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] . Prove that , A^(3)-6A^(2)+5A+11I=0 . Hence find A^(-1) using it .

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

For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}] . Show that A^2-4A-5I=0 Hence find A^(-1)

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

For the matrix A=[{:(2,3),(1,2):}] , show that A^2-4A+I_2=0 . Hence, find A^(-1)

If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] Verify the result A^3-6A^2+9A-4I=O and hence find A^(-1)

For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such that A^2+aA+bI=O

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

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NCERT GUJARATI-DETERMINANTS -EXERCISE 4.5
  1. Find the adjoint of each of the matrices in questions 1 and 2. [{:(1...

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  2. Find the adjoint of the matrices [{:(1,-1,2),(2,3,5),(-2,0,1):}]

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  3. Verify A (adj A) = ( adj A) A= |A| I in Excercises 3 and 4 {:[( 2,3),...

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  4. If A = {:((1,-1,2),(3,0,-2),(1,0,3)):}, verify that A (adj A) = |A|* I...

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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 given below : [(3,-5),(-1,...

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  7. Find the inverse of each of the matrices (if it exists ) {:[( 1,2,3),...

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  8. Find the inverse of each of the matrices (if it exists ) {:[( 1,0,0)...

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  9. Find the inverse of each of the matrices (if it exists ) {:[( 2,1,3...

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  10. Find the inverse of each of the matrices given below : Computer (A...

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  11. Find the inverse the matrix (if it exists)given in[0 0 0 0cosalphasina...

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

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  13. if A=[{:(3,1),(-1,2):}],show that A^(2)-5A+7I=0.

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  14. Solve system of linear equations, using matrix method, x y" "+" "2...

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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+11\ I3=O ...

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  16. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

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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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