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If A = [(cos theta, sin theta),(-sin the...

If `A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)]`, evaluate `A cos theta + B sin theta`.

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. If A = [(1,1),(1,1)], compute A^3

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  2. If A = [(1,2),(-3,0)] and B = [(0,1),(2,3)], compute 2A - B.

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  3. If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin ...

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  4. Find the matrix X such that A + 2 B + X = O, where A = [(3,-2),(1,5)] ...

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  5. Write down a scalar matrix of order 2 whose (2,2)th entry is -1.

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  6. Give an example of a 3xx3 lower triangular matrix.

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  7. If A is of order 5 xx 3, what is the number of elements in a row of A...

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  8. If A is of order mxxn, find the number of elements in a column of A.

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  9. If A is of order mxx2 and both A + B and AB are defined, find m.

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  10. Write the diagonal of the matrix A = [(1,0,2),(2,0,3),(3,6,4)].

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  11. Find the number of all possible matrices of order 2xx2 with entries 0,...

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

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

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

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

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

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

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

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

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