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Define symmetric & skew symmetric matrix...

Define symmetric & skew symmetric matrix and give and example to each.

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Symmetric matrix: A square matrix A is said to be symmetric if `A^(T) = A` skew symmetric matrix: A square matrix A is said to be skew symmetric if `A^(T) = - A`
Ex : `A = [(0,-1),(1,0)]`
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SRISIRI PUBLICATION-IPE SCANNER (TEXUAL BITS)-Very Short Questions (2 marks) (Matrices)
  1. Find the minors of -1 and 3 in the matrix [(2,-1,4),(0,-2,5),(-3,1,3)]

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  2. Find the cofactors of 2 and -5 in the matrix [{:(-1,0,5),(1,2,-2),(-4,...

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  3. Find the determinant of the matrix [(a,h,g),(h,b,f),(g,f,c)]

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  4. Find the determinant of the matrix [{:(a,b,c),(b,c,a),(c,a,b):}]

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  5. P.T the determinant of skew symmetric matrix of order 3 is zero.

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  6. Find the Adjoint and Inverse of the matrix A = [(1,2),(3,-5)]

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  7. Find the Adjoint and Inverse of the matrix [(cos alpha,-sin alpha),(si...

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  8. If A = [(a+ib,c+id),(-c+id,a-ib)], a^(2)+b^(2)+c^(2)+d^(2) =1, then fi...

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  9. Find the rank of the matrix A = [(1,0),(0,1)]

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  10. Find the rank of the matrix A = [(1,1),(0,0)]

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  11. Find the rank of the matrix A = [(1,0,-4),(2,-1,3)]

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  12. Find the rank of the matrix [(1,2,6),(2,4,3)]

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  13. Find the rank of [(1,2,3),(2,3,4),(0,1,2)]

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  14. Define Trace of a matrix.

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  15. What is transpose of a matrix?

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  16. Define a diagonal matrix. Give one example.

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  17. Define a scalar matrix, Give one example.

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  18. Define symmetric & skew symmetric matrix and give and example to each.

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  19. Define Rank of a matrix.

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  20. For any square matrix A, show that AA' is symmetric.

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