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

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

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Find A^2-5A+6I if A=[(2,5,8),(6,0,5),(0,-2,0)]

Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 , 4]][[5, (-1)],[ 6 ,7]] ii) [[1, 2 , 3],[ 0 , 1, 0],[ 1 , 1, 0]][[(-1), 1, 0],[ 0, (-1), 1],[ 2, 3, 4]] ne[[(-1), 1, 0],[ 0, (-1), 1],[ 2, 3, 4]] [[1 , 2, 3],[ 0, 1, 0],[ 1, 1, 0]] .

If A=[[1,-1,1],[2,-1,0],[1,0,0]] , Find A^2

Find X and Y , if X+Y=[[5 , 2],[ 0, 9]] and X-Y=[[3, 6],[ 0 , -1]]

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Compute the indicated products. i) [[a , b],[ -b , a]] [[a, -b],[ b, a]] ii) [[1], [ 2], [3]][[2, 3 ,4]] iii) [[1, (-2)],[ 2 ,3]] [[1 , 2 ,3],[ 2, 3 , 1]] iv) [[2 , 3 , 4 ],[ 3 , 4 , 5 ],[ 4, 5 ,6]] [[1 , -3, 5],[ 0, 2, 4],[ 3, 0, 5]] v) [[2 , 1],[ 3 , 2],[ (-1), 1]] [[1, 0 , 1],[ (-1), 2, 1]] vi) [[3, (-1), 3],[ (-1), 0, 2]][[2, -3],[ 1 , 0],[ 3, 1]]

Find the adjoint of the matrix [[1 , -1, 2],[ 2, 3, 5],[ -2, 0, 1]]

If A =[[1, 2, -3],[ 5, 0, 2],[ 1, -1, 1]], B=[[3, -1, 2],[ 4, 2, 5],[ 2, 0, 3]] and C=[[4 ,1 , 2],[ 0, 3, 2],[ 1, -2, 3]] then compute (A+B) and (B-C) . Also verify that A+(B-C)=(A+B)-C

V PUBLICATION-MATRICES-QUESTION BANK
  1. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  2. Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 ,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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