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Math Help - Solve for X: 2 x 2 matrices.

  1. #1
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    Solve for X: 2 x 2 matrices.

    Hello everyone,

    I am here asking for maths help, the question I have difficult with is question 2 , in my exam practice sheet. Here is the following:

    Exam Revision Questions.jpg

    Requirement:
    Solve for X:

    We know we need to use this method , which are two types:

    Type 1: AX = B and Type 2: XA = B

    But the issue is we must first do operations that will set it up to these two forms.


    We know that we must remove the fraction because Matrices cant divided. I would assume we would times both sides by A to remove the fraction. But the problem is getting those two forms. With these operations.


    Here is my working out: But i don't believe they're correct.

    Workings out.jpg

    So my problem is I cant get AX = B or XA = B. So I can solve for X, If you want anymore details please tell me and I hope posted this in the correct section as well , I apologize if I didn't.

    Kindest Regards,



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  2. #2
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    Opalg's Avatar
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    This is a very badly worded question because it is ambiguous. As you correctly say, matrices can't be divided. The reason for that is that the "quotient" \frac CA should mean the product of C and the inverse of A. But that could be either A^{-1}C or CA^{-1}. Those products are not the same, and so there are two possible solutions to the question.

    If you take the equation (X+B)-\frac CA = 0 and multiply it on the left by A then you get A(X+B) - C = 0, leading to the solution X = A^{-1}(C-AB) = A^{-1}C - B. But if you multiply the original equation on the right by A then it becomes (X+B)A - C = 0, leading to the solution X = (C-BA)A^{-1} = CA^{-1} - B. Those two solutions are different, and they are both equally valid.
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  3. #3
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    Thank you

    well thank you for your respond Opalg.
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