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

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

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The correct Answer is:
`= B^(-1)A^(-1)`
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If A=[{:(3,2),(7,5)],andB=[(-1,-3),(5,2):}] verify that (AB)^(-1)=B^(-1)A^(-1) .

Let A= {:[( 3,7),( 2,5) ]:} and B = {:[( 6,8),( 7,9) ]:} .Verify that (AB) ^(-1) =B^(-1) A^(-1)

If A= {:[( 2,3),( 1,-4) ]:}and B = {:[( 1,-2),( -1,3) ]:} ,then verify that (AB)^(-1) =B^(-1) A^(-1)

If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)] , verify the (A-B)^(T)=A^(T)-B^(T)

If A=[[3,1],[2,5]]B=[[1,2],[2,3]] verify (AB)^(-1)=B^(-1)A^(-1)

If A^(T)=((4,5),(-1,0),(2,3)) and B=((2,-1,1),(7,5,-2)) verify that (A-B)^(T)=A^(T)-B^(T)

If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)] , verify the (B^(T))^(T)=B.

If A=[(5, 2, 9), (1, 2, 8)], B=[(1, 7), (1, 2), (5, -1)] verify that (AB)^(T)=B^(T)A^(T) .

If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)] , verify the (A+B)^(T)=A^(T)+B^(T)=B^(T)+A^(T)

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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