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If A 3xx3 invertible matrix, then show t...

If A `3xx3` invertible matrix, then show that for any scalar 'k' (non-zero), kA is invertible and `(kA)^-1=1/kA^-1`

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. Find the number of all possible matrices of order 2xx2 with entries 0,...

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  2. If A = [(2,3),(1,2)], B = [(1,3,2),(4,3,1)], C = [(1),(2)] and D = [(4...

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  3. If A 3xx3 invertible matrix, then show that for any scalar 'k' (non-ze...

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  4. If [2x,3] {:[(1,2),(-3,0)][(x),(8)]= O, find the value of 'x'.

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  5. If P = [(x,0,0),(0,y,0),(0,0,z)]and Q = [(a,0,0),(0,b,0),(0,0,c)], ver...

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  6. Find x,y if x[(2),(1)] + y[(3),(5)] - [(-8),(-11)] = O

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  7. If possible , find the sum of the matrices of A and B, where A = [(sqr...

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  8. If A = [(cos alpha, - sinalpha),(sinalpha, cosalpha)], then for what v...

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  9. If {:((1,2),(3,4)),((3,1),(2,5)),= ((7,11),(k,23)), then write the val...

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  10. If A = [(2,3),(5,-2), write A^-1 in terms of A.

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  11. If A is a square matrix such that A^2 = A, then write the value of 7A-...

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  12. Solve the following equations for x : [x 1] {:[(1,0),(-2,0)] = 0

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  13. Find x, if any such that [(3,4),(-1,x)] = [(0, x +2),(-1,2)]

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  14. If [{:(a+4,3b),(8,-6):}]=[{:(2a+2,b+2),(8,a-8b):}] write the value of ...

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  15. If matrix A = {:[(2,-2),(-2,2)] and A^2 = lambdaA, then write the valu...

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

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  17. In the matrix A = [[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]], write:...

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  18. In the matrix A = [[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]], write:...

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  19. In the matrix A = [[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]], write:...

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  20. If a matrix has 24 elements, what are the possible orders it can have?...

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