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Math Help - The pair of matrices that are inverses?

  1. #1
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    The pair of matrices that are inverses?

    I need to find the pair of matrices that are inverses, but I don't fully understand how to inverse matrices.

    P = [3 1_-4 0] q = [4 4_12 21]
    R = [0 -1/4_1 3/4]
    S = [7/12 -1/9_-1/3 1/9]
    T = [4 -5 2_8 -1 3]
    U = [-9 6 4_-5 -2 3]
    V = [3 1_0 2_-4 5]

    -------------------------------------------------
    answer choices:

    a. S and R
    b. Q and R
    c. P and Q
    d. Q and S

    if you could explain it to me that would be great, thanks.
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  2. #2
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    Re: The pair of matrices that are inverses?

    You can either,

    Multiply the four choices a,b,c,d out.

    or find each of there determinants.

    If B is the inverse of A then AB= I

    So the answer will be what two matrix multiply together to give the identity matrix.

    Finding their determinants you say B is the inverse of A and Det(A) = 2, then Det(A-1)=Det(B)=1/2

    This means Det(A)Det(B)=1 which means A and B are inverses.

    I'd probably multiply them all out its good practice
    Thanks from Jesssa
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  3. #3
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    Re: The pair of matrices that are inverses?

    Quote Originally Posted by Daniiel View Post
    You can either,

    Multiply the four choices a,b,c,d out.

    or find each of there determinants.

    If B is the inverse of A then AB= I

    So the answer will be what two matrix multiply together to give the identity matrix.

    Finding their determinants you say B is the inverse of A and Det(A) = 2, then Det(A-1)=Det(B)=1/2

    This means Det(A)Det(B)=1 which means A and B are inverses.

    I'd probably multiply them all out its good practice
    I'm also dealing with fractions, which is the main part of the confusion I am having with inverses
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  4. #4
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    Re: The pair of matrices that are inverses?

    Oh okay, with fractions the calculation is a little bit more annoying, but exactly the same process.

    For example a)

    S = [7/12 -1/9_]

    R = [0 -1/4_1 3/4]

    SR =
    7/12 -1/9 ) ( 0 -1/4
    -1/3 1/9 ) ( 1 3/4

    =
    -1/9 (7/12)(-1/4) +(-1/9)(3/4) (can already tell its not I since top r ow isn't 1 0
    1/9 (-1/3)(-1/4) + (-1/3)(3/4)

    So S and R are not inverse,

    alternatively

    Det(S) = 1/36 and Det(R) = -1/4 showing that they are not inverses


    If your still having trouble with fractions one thing you can do is take out factors,

    so R = [0 -1/4_1 3/4] = 1/4 * [0 -1_4 3]

    Then you simply multiply in the fraction after multiplying the matrix to another
    Last edited by Daniiel; April 16th 2012 at 05:51 PM.
    Thanks from Jesssa
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