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if A=[[3, -4],[ 1, (-1)]], then prove...

if `A=[[3, -4],[ 1, (-1)]]`, then prove that
`A^n=[[1+2 n, -4 n ],[n , 1-2n]]`
where `n` is any positive integer.

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BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. A is a third order square matrix and a(ij)={(-i,+,2j,if,i,=,j),(i,x...

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  2. Find the inverse of matrices [(1,-1),(2,3)]

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  3. if A=[[3, -4],[ 1, (-1)]], then prove that A^n=[[1+2 n, -4 n ],[n...

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  4. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

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  5. Using elementary row transformations, find the inverse of the matrix [...

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  6. Let A=[(0,-tanx//2),(tanx//2,0)] Find out I+A and I-A.

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

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  8. A is a third order square matrix and a(ij)={(-i,+,2j,if,i,=,j),(i,x...

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  9. A is a third order square matrix and a(ij)={(-i,+,2j,if,i,=,j),(i,x...

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  10. Let A is a third order square matrix given by a(ij)={(-i+2j, i=j),(ixx...

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  11. A is a third order square matrix and a(ij)={(-i,+,2j,if,i,=,j),(i,x...

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  12. If [(2,-1),(1,0),(-3,4)] A=[(-1,-8,-10),(1,-2,-5),(9,22,15)] Find the ...

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  13. If [(2,-1),(1,0),(-3,4)] A=[(-1,-8,-10),(1,-2,-5),(9,22,15)] Find the ...

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  14. Find the inverse of matrices [(1,-1),(2,3)]

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  15. sin^(-1)(1-x)-2sin^(-1)x= pi/2,then find x

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  16. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

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  17. If [[x-y-z],[-y+z],[z]] = [[0],[5],[3]], then the values of x, y and z...

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  18. If B=[(2,3),(1,0)] find B^2

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  19. If A=[(x,1),(1,0)] ifA^2 is the identity matrix, then find x.

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  20. If U=[2 -3 4],V=[(3),(2),(1)] X=[0 2 3],Y=[(2),(2),(4)] then find UV,X...

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