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Thread: Matrix problem

  1. #1
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    Matrix problem

    I don't even know where to start with this problem, I really don't understand it at all.

    Could anyone help me please?

    Problem:



    Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
    Thanks
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  2. #2
    Senior Member Vinod's Avatar
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    Re: Matrix problem

    Quote Originally Posted by alexdudek View Post
    I don't even know where to start with this problem, I really don't understand it at all.

    Could anyone help me please?

    Problem:



    Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
    Thanks
    Hello,
    $\left[ \begin{matrix}1 &2\\3&2 \end{matrix}\right]-\left[ \begin{matrix}0&1\\1&0\end{matrix}\right]=\left[ \begin{matrix}1&1\\2&2\end {matrix}\right]$ The resultant matrix is not invertible.
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  3. #3
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    Re: Matrix problem

    Quote Originally Posted by alexdudek View Post
    I don't even know where to start with this problem, I really don't understand it at all.

    Could anyone help me please?

    Problem:



    Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
    Thanks
    An invertible 2x2 matrix has no inverse ie determinant is 0.


    sI(subscript 2) is s times the 2x2 identity matrix, ie leading diagonal has elements s and others are 0.


    So find A - sI, find an expression for the determinant, let it equal 0 and solve. (You should end up with a quadratic equation which will yield 2 solutions.) Give it a go.
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  4. #4
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    Re: Matrix problem

    Quote Originally Posted by Vinod View Post
    Hello,
    $\left[ \begin{matrix}1 &2\\3&2 \end{matrix}\right]-\left[ \begin{matrix}0&1\\1&0\end{matrix}\right]=\left[ \begin{matrix}1&1\\2&2\end {matrix}\right]$ The resultant matrix is not invertible.
    This doesn't answer the question asked.
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  5. #5
    Senior Member Vinod's Avatar
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    Re: Matrix problem

    Quote Originally Posted by Debsta View Post
    This doesn't answer the question asked.
    Hello,
    Sorry for providing irrelevant answer.
    $\left[ \begin{matrix} 1&2\\3&2 \end{matrix} \right]$-$\left[ \begin {matrix}-1&0\\0&-1 \end {matrix}\right]$=$\left[ \begin{matrix}2&2\\ 3&3 \end{matrix} \right]$. The resultant matrix is not invertible.
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  6. #6
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    Re: Matrix problem

    Quote Originally Posted by alexdudek View Post
    I don't even know where to start with this problem, I really don't understand it at all.

    Could anyone help me please?

    Problem:



    Find, with explanation, all real numbers s such that the Matrix A - sI2 is NOT invertible
    Thanks
    It is sad that you would be working with matrices and not know that "a matrix is invertible if and only if its determinant is non-zero". So you are looking for s such that $\displaystyle \left|\begin{bmatrix} 1 & 2 \\ 3 & 2\end{bmatrix}- s\begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}\right|= \left |\begin{array}{cc}1- s & 2 \\ 3 & 2- a\end{array}\right|= (1- s)(2- s)- 6\ne 0$.

    The matrix will NOT be invertible when $\displaystyle (1- s)(2- s)- 6= s^2- 3s- 4= 0$. Solve that quadratic equation.
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  7. #7
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    Re: Matrix problem

    Quote Originally Posted by Debsta View Post
    A non- invertible 2x2 matrix has no inverse ie determinant is 0.

    sI(subscript 2) is s times the 2x2 identity matrix, ie leading diagonal has elements s and others are 0.


    So find A - sI, find an expression for the determinant, let it equal 0 and solve. (You should end up with a quadratic equation which will yield 2 solutions.) Give it a go.
    (Edit... sorry)
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