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If A=[[cosalpha,sinalpha],[-sinalpha,cos...

If `A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]]` is such that `A^T=A^(-1)` , find `alpha` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Find the matrix X for which [(1,-4) ,(3,-2)]X=[(-16,-6),( 7, 2)] .

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  2. If A=[[0 ,1 ,3],[ 1, 2,x],[2, 3, 1]] and A^(-1)=[[1//2,-4 ,5//2],[-1//...

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  3. If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1...

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  4. If matrix A=[(0, 2,y),( z, x, y),(-z, x-y, z)] satisfies A^T=A^(-1) ...

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  5. Find the matrix A such that |A|=2 and a d j\ A=[[2, 2, 0],[ 2, 5, 1],[...

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  6. If A is a non-singular matrix, prove that: a d j\ (A) is also no...

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  7. If A is a non-singular matrix, prove that (a d j\ A)^(-1)=(a d j\ A...

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  8. Find the non-singular matrices A , if it is given that a d j\ (A)=[...

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  9. If A=[(2,-1, 1),(-1, 2,-1),( 1,-1, 2)] , find (a d j\ A)^(-1) and (a...

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  10. Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric i...

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  11. Find the adjoint of the following matrices: [(-3, 5),( 2, 4)] Verif...

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  12. Find the adjoint of the following matrices: [(cosalpha,sinalpha),(si...

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  13. Compute the adjoint of each of the following matrices: [[1, 2, 2],[ ...

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  14. For the matrix A=[[1,-1, 1],[ 2 ,3, 0 ],[18 ,2 ,10]] , show that A(a d...

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  15. If A=[[-4,-3,-3],[ 1, 0 ,1],[ 4 ,4, 3]] , show that a d j\ A=A .

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  16. If A=[(-1,-2,-2 ),(2, 1,-2),( 2,-2 ,1)] , show that a d j\ A=3A^T .

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  17. Find A(a d j\ A) for the matrix A=[[1,-2 ,3],[ 0, 2,-1],[-4 ,5, 2]] .

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  18. Find the inverse of the following matrix: |[costheta,sintheta],[-sinth...

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  19. Find the inverse of [(1, 2, 3),( 2, 3, 1),( 3, 1, 2)].

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  20. Find the inverse of [(1, 2, 5),( 1,-1,-1),( 2 ,3,-1)]

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