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If `A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]]`, prove that `A^n=[[3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1) , 3^(n-1), 3^(n-1)]]` `n in N`.

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BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. Consider the matrix A=[(3,10),(2,7)] Express the matrix as A=IA.

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  2. Consider the matrix A=[(3,10),(2,7)] Find A^-1 using elementary row tr...

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  3. If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]], prove that A^n=[[3^(n-...

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  4. If A=[(costheta,sintheta),(-sintheta,costheta)] Find A^2

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  5. If A=[[cos theta, sin theta],[ -sin theta, cos theta]], then prove ...

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  6. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  7. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  8. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  9. Write two non-zero matrices A and B for which AB=0.

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  10. Express A=[(1,-1),(2,3)] as the sum of a symmetric matrix and a skew s...

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  11. Let A=[a(ij)](2times3) where a(ij=i+j. construct A.

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  12. For any square matrix A,prove that A+A' is symmetric.

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  13. If A is a skew symmetric matrix of order 3. Then prove that it's deter...

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  14. Given abs [[2+x,3,4],[1,-1,2],[x,1,5]] is a singular matrix. Find the ...

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  15. Given A and B are square matrices of order 2 such that absA=-1, absB=3...

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  16. For the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)].Find the value of...

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  17. If A=[(3,1),(-1,2)] . Show that A^2-5A+7I=0 Hence find A^4 and A^-1 ...

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  18. Using elementary row operations, find the inverse of the matrix [[1,...

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  19. Find x and y if x[[2],[3]]+y[[-1],[1]]=[[10],[5]]

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

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