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Find the inverse of the matrix [(costh...

Find the inverse of the matrix `[(costheta ,sintheta) ,( -sintheta ,costheta )]` .

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A(i j) is the cofactor of the element a(i j) of the determinant [(2...

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  2. Find the inverse of the matrix [(3 ,-2 ),(-7 , 5)] .

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  3. Find the inverse of the matrix [(costheta ,sintheta) ,( -sintheta ,c...

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  4. If A=[(1 ,-3),( 2, 0)] , write a d j\ A .

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  5. If A=[(a , b),( c, d)] , B=[(1 ,0),( 0, 1)] , find a d j\ (A B) .

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  6. If A=[(3, 1) , ( 2 ,-3)] , then find |a d j\ A| .

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  7. If A=[(2, 3),( 5,-2)], write A^(-1)

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  8. Write A^(-1) for A=[(2, 5) ,( 1 , 3)]

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  9. Use elementary column operation C2->C2+2C1 in the following matrix equ...

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  10. If A is an invertible matrix, then which of the following is not tru...

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  11. If A is an invertible matrix of order 3, then which of the following...

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  12. If A=[(3, 4),( 2,4)] , B=[(-2,-2),( 0,-1)] , then (A+B)^(-1) (a) is a...

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  13. If A=[[a, b],[ c ,d]] , then a d j\ A is (a) [[-d,-b],[-c, a]] (b) [[d...

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  14. If A is a singular matrix, then adj A is a. Singular b. non singular...

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  15. If A, B are two n xx n non-singular matrices, then (1) AB is non-singu...

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  16. If A=[(a , 0) ,(0 ,a)] , then the value of |a d j\ A| is ?

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  17. If A= [ [1, 2] , [-1, 1]] , then det (a d j\ A)) is ?

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  18. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

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  19. For any 2xx2 matrix, if A\ (a d j\ A)=[[10 ,0 ],[0 ,10]] , then |A| is...

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  20. If A^5=O such that A^n != I for 1 <= n <= 4, then (I - A)^-1 is equal ...

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