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If A=[{:(" "1," "0,-2),(" "3,-1," "0),(-...

If `A=[{:(" "1," "0,-2),(" "3,-1," "0),(-2," "1," "1):}],B=[{:(" "0,5,-4),(-2,1," "3),(-1,0," "2):}]" and "C=[{:(" "1," "5,2),(-1," "1,0),(" "0,-1,1):}],`
verify that `A(B-C)=(AB-AC).`

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RS AGGARWAL-MATRICES-Exercise 5C
  1. For the following matrices, verify that A(BC)=(AB)C: (i) A=[{:(1,2,5...

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  2. Verify that A(B+C)=(AB+AC), when (i) A=[{:(1,2),(3,4):}],B=[{:(2," "...

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  3. If A=[{:(" "1," "0,-2),(" "3,-1," "0),(-2," "1," "1):}],B=[{:(" "0,5,-...

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  4. If A=[{:(ab,b^(2)),(-a^(2),-ab):}], show that A^(2)=O.

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  5. If A=[{:(2,-2,-4),(-1," "3," "4),(1,-2,-3):}], show that A^(2)=A.

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  6. (i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I(3...

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  7. If A=[2-1 3 2] and B=[0 4-1 7] , find 3A^2-2B+I .

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  8. If A=[{:(2,-2),(-3," "4):}] then find (-A^(2)+6A).

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  9. If A=[3 1-1 2], show that A^2-5A+7I=0

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  10. Show that the matrix A=[2 3 1 2] satisfies the equation A^3-4A^2+A=O .

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

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  12. If A=[{:(-1,2),(3,1):}], find f(A), where f(x)=x^(2)-2x+3.

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  13. If A=[{:(1,2),(4,-3):}] and f(x)=2x^(3)+4x+5, find f(A).

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  14. Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...

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  15. Solve for x and y, when [{:(3,-4),(1," "2):}][{:(x),(y):}]=[{:(3),(1...

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  16. If A=[{:(3,1),(7,5):}], find x and y such that A^(2)+xI=yA.

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  17. Solve system of linear equations, using matrix method, x y" "+" "2...

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  18. Find the matrix A such that [[5-7,],[-2,3]]A=[[-16,-6],[7,2]].

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  19. Find the matrix A such that A.[{:(2,3),(4,5):}]=[{:(0,-4),(10," "3):}]...

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  20. If A=[{:(1,-1),(2,-1):}],B=[{:(a,-1),(b,-1):}]" and "(A+B)^(2)=(A^(2)+...

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