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If F(alpha)=[[cos alpha,0,sin alpha],[0,...

If `F(alpha)=[[cos alpha,0,sin alpha],[0,1,0],[-sin alpha,0,cos alpha]]`, show that `[F(alpha]^(-1)=F(-alpha)`.

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The correct Answer is:
`=F (-alpha)`
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PREMIERS PUBLISHERS-APPLICATIONS OF MATRICES AND DETERMINANTS -SOLUTION TO EXERCISE 1.1
  1. Find the adjoint of the following : [{:(-3,4),(6,2):}]

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  2. Find the adjoint of the following : [[2,3,1],[3,4,1],[3,7,2]]

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  3. Find the adjoint of the following : (1)/(3)[{:(2,2,1),(-2,1,2),(1,-2...

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  4. Find the inverse (if it exists) of the following [{:(-2," "4),(1,-3)...

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  5. Find the inverse (if it exists) of the following [{:(5,1,1),(1,5,1),...

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  6. Find the inverse (if it exists) of the following [{:(2,3,1),(3,4,1),...

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  7. If F(alpha)=[[cos alpha,0,sin alpha],[0,1,0],[-sin alpha,0,cos alpha]]...

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  8. If A=[[5,3],[-1,-2]], show that A^(2)-3A-7I(2)=O(2) Hence find A^(-1).

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  9. If A=(1)/(9)[{:(-8,1,4),(4,4,7),(1,-8,4):}],"prove that"" "A^(-1)=A^(T...

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  10. If A=[{:(8,-4),(-5," "3):}], verify that A(adj A)= (adj A) A= |A|I(2).

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  11. If A = [{:(3,2),(7,5):}] "and B" = [{:(-1,-3),(5,2):}] "verify that" (...

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  12. If adj (A) = [{:(2,-4,2),(-3," "12,-7),(-2," "0,2):}], find A.

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  13. If adj (A) = [{:(0,-2,0),(6,2,-6),(-3,0,6):}] "find" " "A^(-1).

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  14. Find adj (adj(A)) if adj A = [{:(1,0,1),(0,2,0),(-1,0,1):}].

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  15. A=[[1, tan x],[-tan x,1]], show that A^(T)A^(-1)=[[cos 2x,-sin 2x],[si...

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  16. Find the matrix A for which A[{:(5,3),(-1,-2):}]= [(14,7),(7,7)].

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  17. Given A = A=[{:(1,-1),(2,0):}],B= [(3,-2),(1,1)] "and" " "C= [{:(1,1),...

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  18. If A= [{:(0,1,1),(1,0,1),(1,1,0):}], "show that" A^(-1)=(1)/(2)(A^(2)-...

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  19. Decrypt the received encoded message [2,-3][20,4] with the encryption ...

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