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By using properties of determinants, Sho...

By using properties of determinants, Show that :
`{:|(0,a,-b),(-a,0,-c),(b,c,0)|=0`

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Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2),c^(2)),( bc,ca,ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a)

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MODERN PUBLICATION-MATRICES-EXERCISE
  1. Show that the matrix A = [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric m...

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  2. Show that the matrix A = [[0,1,-1],[-1,0,1],[1,-1,0]] is a skew symmet...

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  3. By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-...

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  4. Show that A + A^T is symmetric matrix, where A^T denotes the tranpose ...

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  5. Show that A + A^T is symmetric matrix, where A^T denotes the tranpose ...

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  6. Show that A + A^T is symmetric matrix, where A^T denotes the tranpose ...

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  7. Show that A - A^T is symmetric matrix, where A^T denotes the tranpose ...

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  8. A matrix denotes a number

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  9. Check whether A - A^T is symmetric matrix, where A^T denotes the tranp...

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  10. Express the matrix A as sum of symmetric and skew symmetric matrix ...

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

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

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

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

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

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

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

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

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

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