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Find A^2 if A= [(cos alpha, sinalpha),(-...

Find `A^2` if A`= [(cos alpha, sinalpha),(-sin alpha, cos alpha)]`

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If A = [(cos alpha sin alpha),(-sinalpha, cosalpha)] , prove (by inducton ) that A^n = [(cos n alpha, sinnalpha),(-sin n alpha cosn alpha)] for all positive integral n.

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. If A is of order 2 xx 3. Is it possible to compute A^2?

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  2. Find x if [(x^2),(9)] - 3 [(x),(9)] = [(-2),(-18)]

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  3. Find A^2 if A= [(cos alpha, sinalpha),(-sin alpha, cos alpha)]

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  4. If A = [1 2 3], evaluate A^t.

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  5. if A = [a b c], evaluate A^TA.

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  6. If A = [(1,2,-1),(x, 3, y),(-1,6,4)] is a symmetric matrix, find x,y.

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  7. If A is a skew symmetric matrix of order 3, write down its (2,2)th ele...

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  8. If A = [(1,2),(2,4)], find A^-1

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  9. If A = [(3,5),(1,2)], find A^-1

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  10. If A of order 2 xx 2, state whether 1/2 (A + A^T) is symmetric or skew...

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  11. If A = [(1,1),(1,1)], compute A^3

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

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

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

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

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

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

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

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

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

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