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If A=[(3,-4),(1,-1)] prove that A^k=[(1+...

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

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MOTION-MATRICES -Exercise - 3(Subjective - type Questions)
  1. If [{:(,x-y,1,z),(,2x-y,0,w):}]=[{:(,-1,1,4),(,0,0,5):}], "find x,y,z,...

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  2. If A=[{:(,1,2),(,3,-4),(,5,6):}]and B=[{:(,4,5,6),(,7,-8,2):}] will AB...

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  3. If A=[(3,-4),(1,-1)] prove that A^k=[(1+2k,-4k),(k,1-2k)] where k is a...

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  4. If A=[{:(,2,-1),(,3,4):}]=B=[{:(,5,2),(,7,4):}],C=[{:(,2,5),(,3,8):}] ...

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  5. If A and B are non-zero square matrices of same order such that AB=A a...

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  6. If A=[(ab,b^2),(-a^2,-ab)], then A is

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  7. If, E=[(0,1,0),(0,0,1),(0,0,0)]and F=[(0,0,0),(1,0,0),(0,1,0)] calcula...

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  8. A is a square matrix of order n. l = maximum number of distinct ent...

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  9. (i) Prove that (adj adj A) = |A|^(n – 2) A (ii) Find the value of |...

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  10. For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0....

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  11. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  12. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

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  13. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

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  14. Compute A^(-1) for the following matrix A=[(-1,2,5),(2,-3,1),(-1,1,1)...

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  15. For the matrix A=[(4,-4,5),(-2,3,-3),(3,-3,4)] find A^(-2) .

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  16. Gaurav purchases 3 pens, 2 bags and 1 instrument box and pays Rs. 41. ...

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  17. Solve the following system of linear equations by using the principle ...

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  18. Solve the following system of linear equations by using the principle ...

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  19. By using the principle of matrix, show that the following system of eq...

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  20. Find the number of 2xx2 matrix satisfying (i) aij is 1 or -1 (ii) ...

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