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Math Help - Triangular Matrix

  1. #1
    VkL
    VkL is offline
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    Triangular Matrix

    Find all real triangular matrices A such that A^2 = B

    |2 21|
    |0 25|




    |
    | --> Matrix!! not det, or absolute value.

    How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by VkL View Post
    Find all real triangular matrices A such that A^2 = B

    |2 21|
    |0 25|
    Is this B? If A is an upper triangular matrix \begin{bmatrix}a & b \\ 0 & c\end{bmatrix}, then [tex]A^2= a^2 & ab+ bc \\ 0 c^2\end{bmatrix}= \begin{bmatrix}2 & 21 \\ 0 & 25\end{bmatrix}.

    So you need to solve a^2= 2, ab+ bc= 21, and c^2= 25. It should be easy to solve for a and c and then you have a simple linear equation to solve or b. Nothing could be simpler!



    |
    | --> Matrix!! not det, or absolute value.

    How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?[/QUOTE]
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  3. #3
    MHF Contributor

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    Quote Originally Posted by VkL View Post
    Find all real triangular matrices A such that A^2 = B

    |2 21|
    |0 25|
    Is this B? If A is an upper triangular matrix \begin{bmatrix}a & b \\ 0 & c\end{bmatrix}, then A^2= \begin{bmatrix}a^2 & ab+ bc \\ 0 & c^2\end{bmatrix}= \begin{bmatrix}2 & 21 \\ 0 & 25\end{bmatrix}.

    So you need to solve a^2= 2, ab+ bc= 21, and c^2= 25. It should be easy to solve for a and c and then you have a simple linear equation to solve or b. Nothing could be simpler!



    |
    | --> Matrix!! not det, or absolute value.

    How do I approach this? I htought about getting rid of the 25 on the bottom right to make it a triangular matrix. Then what?
    ???? Even with the "25", that is triangular!
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