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Construct a 2xx2 matrix A=[a(i j)] whose...

Construct a `2xx2` matrix `A=[a_(i j)]` whose elements `a_(i j)` are given by `a_(i j)={(|-3i+j|)/2,\ \ if\ i!=j(i+j)^2,\ \ if\ i=j`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Write a 2xx2 matrix which is both symmetric and skew-symmetric.

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  2. If [(x y,4),(z+6,x+y)]=[(8,w),(0, 6)] , write the value of (x+y+z) .

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  3. Construct a 2xx2 matrix A=[a(i j)] whose elements a(i j) are given by ...

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  4. If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

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  5. Matrix A=[(0, 2b,-2) ,(3 ,1, 3), (3a,3,-1)] is given to be symmetric, ...

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  6. Write the number of all possible matrices of order 2xx2 with each e...

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  7. If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order o...

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  8. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

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  9. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

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  10. If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) ...

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  11. If A and B are two matrices such that A B=A and B A=B , then B^...

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  12. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

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  13. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

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  14. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

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  15. If the matrix A B is zero, then It is not necessary that either A=O...

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  16. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

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  17. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

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  18. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

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  19. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals (a)[(1,n a),(0, ...

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  20. If A=[[1, 2, x], [0 ,1 ,0],[ 0, 0, 1]] and B=[[1,-2,y],[0, 1, 0 ],[0...

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