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If A = [[cos alpha,sin alpha],[-sin alph...

If `A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]]` , then verify that `A'A = I`

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MODERN PUBLICATION-MATRICES-EXERCISE
  1. Express the matrix A as sum of symmetric and skew symmetric matrix ...

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  2. If A = {:[(1,2,3),(-1,0,2),(1,-8,-1)], B = [(4,5,6),(-1,0,1),(2,1,2)],...

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  3. If A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]] , then verify th...

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  4. If A = [[sin alpha,cos alpha],[-cos alpha,sin alpha]], then verify tha...

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  5. Show that (AB)' = B'A' A = {:[(-1,3,0),(-7,2,8)], B = [(-5,0),(0,3),...

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  6. Show that (AB)' = B'A' A = {:[(3,4),(4,5)], B = [(5,3),(2,1)].

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  7. If A = {:[(-5,1),(6,8)], B = [(2,1),(3,4)], C = [(1,3),(-1,4)] verify ...

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  8. If A = {:[(5,-1),(6,7)], B = [(2,1),(3,4)], C = [(1,3),(-1,4)] verify ...

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  9. If A = {:[(5,-1),(6,7)], B = [(2,1),(3,4)], C = [(1,3),(-1,4)] verify ...

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  10. If A = {:[(5,-1),(6,7)], B = [(2,1),(3,4)], C = [(1,3),(-1,4)] verify ...

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  11. If A and B are symmetric matrices, prove that AB – BA is a skew symmet...

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  12. For a matrix A=[(3,2),(5,3)],Verify that : A + A' is a Symmetric Mat...

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  13. Verify that : A - A' is a Skew - symmetric Matrix. When : A = {:[(...

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  14. Verify that : A - A' is a Skew - symmetric Matrix. When : A = {:[(...

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  15. Verify that : A - A' is a Skew - symmetric Matrix. When : A = {:[(...

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  16. Verify that : A - A' is a Skew - symmetric Matrix. When : A = {:[(...

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  17. For the matrix A=[(1,5),(6,7)], verify that (A+A') is a symmetric matr...

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  18. For the matrix A= ((1,5),(6,7)) , verify that : A - A' is a Skew-Symme...

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  19. If A = {:[(3,1,-1),(0,1,2)], then show that AA' is a symmetric matrix.

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  20. Find (1)/(2)(A+A')and(1)/(2)(A-A'), when A=[(0,a,b),(-a,0,c),(-b,-c,0)...

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