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If F (x) = [[cos x,-sin x,0],[sin x, cos...

If `F (x) = [[cos x,-sin x,0],[sin x, cos x, 0],[0,0,1], then show that F(x) F(y)= F (x+y).

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PRADEEP PUBLICATION-MATRICES-EXERCISE
  1. If x [[2],[3]]+y[[-1],[1]]=[[10],[5]], then find the value of x and y.

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  2. Given3[[x,y],[z,w]] = [[x,6],[-1,2w]] + [[4,x+y],[z+w,3]] , find the v...

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  3. If F (x) = [[cos x,-sin x,0],[sin x, cos x, 0],[0,0,1], then show that...

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  4. Show that: [[5,-1],[6,7]][[2,1],[3,4]] ne [[2,1],[3,4]][[5,-1],[6,7]]

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  5. Show that: [[1,2,3],[0,1,0],[1,1,0]][[-1,1,0],[0,-1,1],[2,3,4]] ne [[...

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  6. If A = {:[(2,0,1),(2,1,3),(1,-1,0)], then find A^2 - 5A 6I

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  7. If A = [[1,0,2],[0,2,1],[2,0,3]] , prove that A^3 -6A^2 +7A + 2I = 0

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  8. If A = [ (3,-2),(4,-2)] and I = [(1,0),(0,1)] , then find k so that A...

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  9. If A = [[0,-tan alpha/2],[tan alpha/2,0]] and I is the identity matrix...

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  10. A trust fund has Rs. 30,000 that must be invested in two different typ...

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  11. A trust fund has Rs. 30,000 that must be invested in two different typ...

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  12. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  13. Assume X, Y, Z, W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 ...

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  14. Find the transpose of each of the followig matrices. [(5),(1/2),(-1)...

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  15. Find the transpose of each of the followig matrices. [(1,-1),(2,3)]

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  16. Find the transpose of each of the following matrices: {:[(-1,5,6),(s...

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  17. If A = {:[(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1...

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  18. If A = [[-1,2,3],[5,7,9],[-2,1,1]] and B = [[-4,1,-5],[1,2,0],[1,3,1]]...

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  19. If A' = [(3,4),(-1,2),(0,1)] and B = [(-1,2,1),(1,2,3)], then porve th...

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  20. If A' = [(3,4),(-1,2),(0,1)] and B = [(-1,2,1),(1,2,3)], then porve th...

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