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State'True'or'false':For any square matrix A, AA' is symmetric.

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State ‘True’ or ‘False’. For any square matrix A, A+A' is symmetric.

State'True'or'false':For any square matrix (A-A^1)^2 is skew symmetric.

State ‘True’ or ‘False’. For any square matrix A, A-A' is skew symmetric.

State'True'or'false': A matrix which is not symmetric is skew symmetric.

State'True'or'false':If A is symmetric then A-A^1 is both symmetric and skew symmetric.

State'True'or'false':If A and B are symmetric matrices of the same order and AB-BA !=0 , then AB is not symmetric

State'True'or'false':If A is any skew symmetric matrix, then A^2 is also skew symmetric.

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USHA PUBLICATION-MATRICES DETERMINANTS PROBABILITY -EXERCISE
  1. If A is a 2xx2 non-singular matrix and absA=1/2 then which matrix is r...

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  2. What is the order of the matrix B if[" 3"" 4"" 2 ""] B =[ 2 "" 1"" 0""...

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  3. State'True'or'false':For any square matrix A, AA' is symmetric.

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  4. State ‘True’ or ‘False’. For any square matrix A, A+A' is symmetric.

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  5. State ‘True’ or ‘False’. For any square matrix A, A-A' is skew symmetr...

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  6. If A is a 4xx5 matrix and B is a matrix such that A^TB and BA^T both a...

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  7. If A and B are two square matrices of same order, then (A+B)^2=A^2+2AB...

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  8. 1.Solve for x: abs ((1,1,x),(p+1,p+1,p+x),(3,x+1,x+2))=0

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  9. Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

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  10. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  11. Without expanding,show that the following determinant vanishes. abs((2...

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  12. Without expanding,show that the following determinant vanishes. abs ((...

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  13. Without expanding,show that the following determinant vanishes. abs((b...

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  14. Without expanding,show that the following determinant vanishes. abs((6...

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  15. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

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  16. If a, b and c are all positive real, then prove that minimum value of ...

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  17. Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

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  18. Prove that: |[a, b, c],[a-b, b-c, c-a ], [b+c, c+a, a+b]|= a^3+b^3+c^3...

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  19. Solve by cramer's rule :2x+3y=6, 4x+6y=12

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  20. If A=[[ 3,-5,],[-4,2,]],show that A^2-5A-14I=O,where I is a unit matri...

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