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If `A=[[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]]`, prove that `A^3-6 A^2+7 A+2I=0`

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V PUBLICATION-MATRICES-QUESTION BANK
  1. Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 ,...

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  2. Find A^2-5 A+6 I, if A=[[2, 0, 1],[ 2 ,1 , 3],[ 1, -1, 0]]

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  3. If A=[[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]], prove that A^3-6 A^2+7...

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  4. If A=[[3,-2],[4,-2]] and I=[[1,0],[0,1]], find k so that A^2=kA-2I

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  5. If A=[[0, -tan (alpha/2)], [ tan (alpha/2), 0]] and I is the identi...

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  6. A trust fund has Rs. 30,000 that must be invested in two different typ...

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  7. The bookshop of a particular school has 10 dozen chemistry books, 8 do...

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  8. Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nx...

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  9. Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx...

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  10. If A=[[3 ,sqrt3, 2],[ 4 , 2, 0]] and B=[[2 , (-1), 2],[ 1, 2, 4...

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  11. If A=[[-2],[4],[5]] B=[[1,3,6]] (AB)^T=B^TA^T

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  12. For any square matrix A with real number entries.Prove that A+A^' is a...

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  13. Prove that any square matrix can be expressed as the sum of a symmetic...

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  14. Express the matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a ...

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  15. Find the transpose of each of the following matrices: (i) [[5], [1/2]...

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  16. If A=[[-1, 2, 3],[ 5, 7, 9],[ -2, 1 , 1]] and B=[[-4 , 1, -5],[ ...

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  17. If A^'=[[3, 4],[ -1, 2],[ 0, 1]] and B=[[-1, 2 , 1],[ 1,2, 3]] ...

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  18. If A^'=[[-2, 3],[ 1, 2]] and B=[[-1, 0],[ 1, 2]], then find (A+2...

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  19. For the matrices A and B verify that, (AB)^'=B^' A^', where i) A=[[1...

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  20. if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]], then verify A^T...

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