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DLS

  • 2 years ago

Matrix help!

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  1. DLS
    • 2 years ago
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    \[If~A=\left[\begin{matrix}\alpha & 0 \\ 1 & 1\end{matrix}\right] \] \[\And~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right]\] such that \[A^2=B\] Then \[\alpha=?\]

  2. DLS
    • 2 years ago
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    Options: A)1 B)-1 C)4 D)None of these

  3. DLS
    • 2 years ago
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    \[\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]\] I am getting this after equating A^2=B I am getting all the 3 options A,B,C. But it is a single choice question.

  4. DLS
    • 2 years ago
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    @yrelhan4

  5. DLS
    • 2 years ago
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    @agent0smith @dmezzullo @electrokid

  6. phi
    • 2 years ago
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    the lower left entry should be in B is 0. so you have a^2 =1 and a+1=0

  7. DLS
    • 2 years ago
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    no..

  8. phi
    • 2 years ago
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    are you sure about the B matrix? A*A is [ a^2 0 ] [ a+1 1 ] which cannot match B as given

  9. DLS
    • 2 years ago
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    yes i checked twice

  10. phi
    • 2 years ago
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    which version of B is the one given? the original or the one you posted later?

  11. agent0smith
    • 2 years ago
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    \[~B=\left[\begin{matrix}1 & 5 \\ 0 & 1\end{matrix}\right] \] \[\LARGE \left[\begin{matrix}\alpha^2 & 0 \\ \alpha+1& 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 5 & 1\end{matrix}\right]\] which is B...

  12. DLS
    • 2 years ago
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    later one sorry

  13. agent0smith
    • 2 years ago
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    so alpha^2 = 1 and alpha+1 = 5...??? that doesn't seem to work :/

  14. phi
    • 2 years ago
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    as you noticed, there is no unique solution for alpha...

  15. DLS
    • 2 years ago
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    A,B,C all 3 are correct but single choice .-.

  16. agent0smith
    • 2 years ago
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    If you're sure that second matrix is right, then there's no solution. The first matrix would give alpha is -1.

  17. phi
    • 2 years ago
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    I think you should choose option D

  18. DLS
    • 2 years ago
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    yes it is right :| the solution says none of these since this is an absurd case :O

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