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Math Help - [SOLVED] some matrices help

  1. #1
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    [SOLVED] some matrices help

    hi, some more matrices problems that i can't solve
    no 1 :

    a) Find PQ which i did =

    i can't solve b which is

    b) Find a matrix X such that PX + Q = P




    no2) If work out x^{2} and X ^{3}

    hence show that X^{3} = 4X - X^{2} + I

    i worked out x^2 and X^3 , and i tried doing the above calculations but didn't get x^3
    what should i do?

    thanks in advance
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  2. #2
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    For #1b you must first find P^{-1}.
    Then X=P^{-1}(P-Q).

    #2 is just a matter of doing all the caculations correctly.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by llkkjj24 View Post
    no2) If work out x^{2} and X ^{3}

    hence show that X^{3} = 4X - X^{2} + I

    i worked out x^2 and X^3 , and i tried doing the above calculations but didn't get x^3
    what should i do?

    thanks in advance
    Hi llkkjj24,

    X=\left[\begin {array}{ccc}1 & 0 & 1 \\ 0 & -2 & 1 \\ 1 & 1 & 0 \end{array}\right] \: \: X^2=\left[\begin {array}{ccc}2 & 1 & 1 \\ 1 & 5 & -2 \\ 1 & -2 & 2 \end{array}\right]\: \: X^3=\left[\begin {array}{ccc}3 & -1 & 3 \\ -1 & -12 & 6 \\ 3 & 6 & -1 \end{array}\right]

    X^3=4X-X^2+I


    \left[\begin {array}{ccc}3 & -1 & 3 \\ -1 & -12 & 6 \\ 3 & 6 & -1 \end{array}\right]=4\left[\begin {array}{ccc}1 & 0 & 1 \\ 0 & -2 & 1 \\ 1 & 1 & 0 \end{array}\right]-\left[\begin {array}{ccc}2 & 1 & 1 \\ 1 & 5 & -2 \\ 1 & -2 & 2 \end{array}\right]+\left[\begin {array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]
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  4. #4
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    As Plato points out, you need to know the inverse of P to solve the first part. Did you notice what the value of PQ is? If so, what is Q?
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  5. #5
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    thanks, i noticed for no1 i did a mistake, i multiplied x^2 with x^2 instead of multiplying it with X to get x^3
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  6. #6
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    Quote Originally Posted by qmech View Post
    As Plato points out, you need to know the inverse of P to solve the first part. Did you notice what the value of PQ is? If so, what is Q?
    yes, Q is the inverse of P
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  7. #7
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    thanks guys, problem solved
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