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    Linear Algebra
    Matrices
    Eigen Values and Eigen Vectors(I)

    Find the characteristic equation of the matrix

    A = [1, 3, 7; 4, 2, 3; 1, 2, 1]

    Show that the equation is satisfied by and hence obtain the inverse of the given matrix.

    The fully formatted problem is in the attached file.

    © BrainMass Inc. brainmass.com October 2, 2022, 6:43 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/characteristic-equation-matrix-inverse-matrix-45432

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    Linear Algebra
    Matrices
    Eigen Values and Eigen Vectors(I)

    By:- Thokchom Sarojkumar Sinha

    Find the characteristic equation of the matrix

    Show that the equation is satisfied by and hence obtain the inverse of the given matrix.

    Solution:- The characteristic equation of is

    i.e.,

    or,

    or,

    or,

    or,

    or,

    or.,

    or, ----------------------------------(1)
    which is the required characteristic equation of .

    Since by Cayley Hamilton Theorem, every square matrix satisfies its own characteristic
    equation.
    Hence the matrix must satisfy its characteristic equation.

    i.e., ----------------------------------(2)
    where is the unit matrix of order 3.

    We have to show the above relation.

    L.H.S. of (2)

    = R.H.S. of (2)

    Hence shown.

    Again, we have

    Multiplying both sides of the above equation by , we get

    or,

    or,

    Therefore

    --------------------------------------------------------------------------------------------

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