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If A=[[cosalpha,-sinalpha,0],[sinalpha,c...

If `A=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]]` , find `a d j\ A` and verify that `A(a d j\ A)=(a d j\ A)A=|A|I_3` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A=|[3, 0,-1], [2, 3 ,0], [0, 4, 1]| , then find |a d j\ (a d j\ A)|...

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  2. If A=|[a, b], [c ,d]| , find a d j\ A .

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  3. If A=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]] , find ...

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  4. If A=|[2, 3], [5,-2]| , show that A^(-1)=1/(19)Adot

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  5. Find the inverse of A=[[1, 3, 3],[ 1, 4, 3],[ 1, 3, 4]] and verify tha...

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  6. If A=|[1,tanx],[-tanx,1]| , show that A^T\ A^(-1)=|[cos2x,-sin2x],[sin...

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  7. If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=...

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  8. Show that A=|[2,-3], [3 ,4]| satisfies the equation x^2-6x+17=0 . Henc...

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  9. For the matrix A=|[3, 1], [7, 5]| , find x and y so that A^2+x I=y Ado...

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  10. For the matrix A=[[3, 2],[ 1, 1]] , find the numbers a and b such that...

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  11. Show that the matrix A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]] satisfies the...

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  12. If A=[[1,-1, 1],[ 2,-1, 0],[ 1, 0, 0]] , show that A^(-1)=A^2 .

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  13. Find a 2xx2 matrix B such that B[(1,-2),( 1, 4)]=[(6, 0),( 0, 6)] .

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  14. Find the matrix A satisfying the matrix equation [(2, 1),( 3, 2)]A...

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  15. Find the matrix X for which [(1,-4) ,(3,-2)]X=[(-16,-6),( 7, 2)] .

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

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

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

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

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

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