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Eigenvalue Calculator
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Eigenvalue calculator is an online mathematical tool to determine the eigenvalues of a square matrix. In this calculation, we have to consider the unit matrix with same order of the given matrix. Eigenvalue can be represented using the symbol λ.

Default 3 x 3 matrix is given in the first calculator below. The calculator will find the eigenvalues on clicking "Calculate Eigenvalues", satisfying the characteristic equation of the given matrix. Eigenvalues for 2 x 2 matrix is also calculated as per the 3 x 3 matrix.
 

Steps for Eigenvalue Calculator

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Step 1 :  

Name the given matrix as A.



Step 2 :  

Let consider a unit matrix of same order of A.



Step 3 :  

Determine the values of λ which satisfy the characteristic equation of the given matrix A. For this calculation, we have to determine the value of λI and A-λI.



Step 4 :  

Find the value of λ, if det(A-λI)=0.



Problems on Eigenvalue Calculator

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  1. Find the eigen values of $\begin{pmatrix}4 &0 \\ 2& 2 \end{pmatrix}$


    Step 1 :  

    Let the given matrix be,


    A=$\begin{pmatrix} 4 &0 \\  2& 2 \end{pmatrix}$



    Step 2 :  

    Consider a unit matrix I which is equal to,


    I=$\begin{pmatrix} 1 &0 \\ 0& 1 \end{pmatrix}$



    Step 3 :  

    To determine the value of λ,


    λI=$\begin{pmatrix} λ &0 \\  0& λ \end{pmatrix}$


    A-λI=$\begin{pmatrix} 4-λ &0 \\  2& 2-λ \end{pmatrix}$



    Step 4 :  

    det(A-λI)=(4-λ)(2-λ)-0=0


    That is, (4-λ)(2-λ)=0


    So, λ=4, λ=2



    Answer  :  

    Eigenvales, λ=4, λ=2



  2. Find the eigen values of $\begin{pmatrix} 2 &1 \\  6& 3 \end{pmatrix}$


    Step 1 :  

    Let the given matrix be,


    A=$\begin{pmatrix} 2 &1 \\  6& 3 \end{pmatrix}$



    Step 2 :  

    Consider a unit matrix I which is equal to,


    I=$\begin{pmatrix} 1 &0 \\  0& 1 \end{pmatrix}$



    Step 3 :  

    To determine the value of λ,


    λI=$\begin{pmatrix} λ &0 \\  0& λ \end{pmatrix}$


    A-λI=$\begin{pmatrix} 2-λ &1 \\  6& 3-λ \end{pmatrix}$



    Step 4 :  

    det(A-λI)=(2-λ)(3-λ)-6=0


    That is, 6-2λ-3λ+λ2-6=0


    λ2-5λ=0


    λ(λ-5)=0


    So, λ=0, λ=5



    Answer  :  

    Eigenvales, λ=0, λ=5



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