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A={:[( 1,1,1),(1,2,-3),(2,-1,3)]:} S...

`A={:[( 1,1,1),(1,2,-3),(2,-1,3)]:} `
Show that `A^(3) - 6A^(2) +5A +11 I =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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If A= {:[( 2,-1,1),(-1,2,-1),(1,-1,2) ]:} Verify that A^(3) -6A^(2) +9A -4I=O and hence find A^(-1)

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NCERT TAMIL-DETERMINANTS -EXERCISE 4.5
  1. Find adjoint of each of the matrices {:[( 1,2),( 3,4)]:}

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

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

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

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  5. Find the inverse of each of the matrices (if it exists ) {:[( -1,5),...

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

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

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

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

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

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  11. Let A= {:[( 3,7),( 2,5) ]:} and B = {:[( 6,8),( 7,9) ]:} .Verify t...

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

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  13. For the matrix A={:[( 3,2),( 1,1) ]:} . Find the numbers a and b suc...

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

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  15. If A= {:[( 2,-1,1),(-1,2,-1),(1,-1,2) ]:} Verify that A^(3) -6A^...

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

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

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