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Find the inverse of the following matrix...

Find the inverse of the following matrix: `|[costheta,sintheta],[-sintheta,costheta]|`

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

Choose the correct answer from the following : The value of |{:(-costheta,sintheta),(-sintheta,-costheta):}| is:

Prove: (costheta)/(1+sintheta)=(1-sintheta)/(costheta)

Statement 1: If A is an orthogonal matrix of order 2, then |A|=+-1. Statement 2: Every two-rowed real orthogonal matrix is of any one of the forms [[costheta ,-sintheta ],[sintheta ,costheta]]or[[costheta ,sintheta],[ sintheta,-costheta]]dot

if A= [{:(costheta,sintheta),(-sintheta,costheta):}], then A A^T =?

If {:A=[(cos theta,sintheta),(-sintheta,costheta)]:}," then A.A' is

Prove: (costheta)/(1-sintheta)=(1+sintheta)/(costheta)

If A=[[costheta,-sintheta],[sintheta,costheta]] then show that A^n = [[cosntheta,-sinntheta],[sinntheta,cosntheta]]

Prove: (1-costheta)/(sintheta)=(sintheta)/(1+costheta)

Simplify the following : cos theta [{:(costheta,-sintheta ),(sintheta,costheta ):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A=[(-1,-2,-2 ),(2, 1,-2),( 2,-2 ,1)] , show that a d j\ A=3A^T .

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

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

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

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

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  6. Find the inverse of [(2,-1, 1),(-1, 2,-1),( 1,-1, 2)]

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  7. Find the inverse of [(2, 0,-1),( 5, 1, 0),( 0, 1, 3)]

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  8. Find the inverse of [(0 ,1,-1),( 4,-3, 4),( 3,-3, 4)]

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  9. Find the inverse of [(0, 0,-1), (3 ,4 ,5),(-2,-4,-7)]

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  10. Find the inverse of [(1, 0, 0),( 0,cosalpha,sinalpha),(0,sinalpha,-cos...

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  11. Find the inverse following matrix and verify that A^(-1)A=I3 . [(1, ...

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  12. Find the inverse following matrix and verify that A^(-1)A=I3 . [(2, ...

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  13. For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1)...

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  14. For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1...

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  15. Let A=[(3, 2),( 7, 5)] and B=[(6, 7),( 8, 9)] . Find (A B)^(-1)

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  16. Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .

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  17. If A=[(4, 5),( 2 ,1)] , then show that A-3I=2(I+3A^(-1))

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  18. Find the inverse of the matrix A=[(a, b),( c,(1+b c)/a)] and show th...

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  19. Given A=[(5, 0, 4),( 2, 3, 2),( 1, 2, 1)] , B^(-1)=[(1, 3, 3),( 1, 4, ...

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  20. Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[...

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