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Show that positive odd integral powers o...

Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

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To show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric, we can follow these steps: ### Step 1: Definition of Skew-Symmetric Matrix Let \( A \) be a skew-symmetric matrix. By definition, this means: \[ A^T = -A \] ...
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STATEMENT -1 All positive odd integral powers of a skew - symmetric matrix are symmetric. STATEMENT-2 : All positive even integral powers of a skew - symmetric matrix are symmetric. STATEMENT-3 If A is a skew - symmetric matrix of even order then |A| is perfect square

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Express the matrix A = [{:(4, 2,-1),(3,5,7),(1,-2,1):} ] as the sum o...

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  2. A matrix which is both symmetric as well as skew-symmetric is a null ...

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  3. Show that positive odd integral powers of a skew-symmetric matrix are ...

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  4. Show that all positive integral powers of a symmetric matrix are sy...

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  5. If B is a skew-symmetric matrix, write whether the matrix A BA^T is sy...

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  6. If matrix A=[a(ij)](2X2), where a(ij)={[1,i!=j],[0,i=j]}, then A^2 i...

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  7. Find the value of lambda, a non-zero scalar, if lambda[(1 ,0, 2),( 3,4...

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  8. Solve the matrix equation [(x^2),(y^2)]-3[(x),(2y)]=[(-2) ,(9)]

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  9. If A ,Ba n dC three matrices of the same order, then prove that A=B ...

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  10. Find non-zero values of x and z satisfying the matrix equation : x[[2x...

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  11. Find a matrix A ,if A+[[2 ,3],[ -1, 4]]=[[3,-6],[-3, 8]]

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  12. If A=d i ag(1-1 2) and B=d i ag(2 , 3 -1), find A+B ,3A+4Bdot

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  13. If A=[[ 2, -1],[3 , 1]] and B=[[1, 4],[7, 2]], find 3A-2B

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  14. Find the values of a and b if A=B , where A=[[a+4,3b],[8,-6]],B=[[2a+2...

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  15. Find the values of x and y if [[x+10,y^2+2y],[0,-4]]=[[3x+4,3],[ 0,y^2...

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  16. For what values of x and y are the following matrices equal? A=[(2x+1,...

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  17. Let A ,B be two matrices such that they commute. Show that for any pos...

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  18. Let A=[[2,3],[-1,2]] and f(x)=x^2-4x+7 Show that f(A)=0 Use this resul...

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  19. If A=[3 5],B=[7 3], then find a non-zero matrix C such that AC=B...

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  20. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+Idot

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