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Math Help - Matrix problem: Finding all matrices A such that AM = - MA

  1. #1
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    Matrix problem: Finding all matrices A such that AM = - MA

    Hiya, I'm stuck on this question and would be really grateful if someone could help me out here...

    Let M = \begin{bmatrix}7 & -3\\15 &-7 \end{bmatrix}. Find all 2x2 matrices A = \begin{bmatrix}a & b\\b &d \end{bmatrix} such that AM = - MA. (Note that the solutions wanted should have equal (1,2)- and (2,1)- entries b.)

    I tried evaluating the equation AM= -MA via matrix multiplication and making equations out of the corresponding entries but ended up with something that just seemed completely wrong AND didn't have equal (1,2)- and (2,1)- entries.

    Please help! Thanks in advance,

    rorosingsong.
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  2. #2
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    Quote Originally Posted by rorosingsong View Post
    Hiya, I'm stuck on this question and would be really grateful if someone could help me out here...

    Let M = \begin{bmatrix}7 & -3\\15 &-7 \end{bmatrix}. Find all 2x2 matrices A = \begin{bmatrix}a & b\\b &d \end{bmatrix} such that AM = - MA. (Note that the solutions wanted should have equal (1,2)- and (2,1)- entries b.)

    I tried evaluating the equation AM= -MA via matrix multiplication and making equations out of the corresponding entries but ended up with something that just seemed completely wrong AND didn't have equal (1,2)- and (2,1)- entries.

    Please help! Thanks in advance,

    rorosingsong.
    Your method is correct just be really careful.

    Here is a .pdf No work is shown but it does have the correct answer. It is a maple screen shot.

    Matrix.pdf
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  3. #3
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    oh wow, thanks so much!
    I'll be more careful with the working this time. Cheers, I really appreciate your prompt reply, very helpful. =)
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