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    Cofactor

    Result

    (-9 | 18 | -9 6 | -12 | 6 -3 | 6 | -3)

    Dimensions

    3 (rows) × 3 (columns)

    Matrix plot

    Transpose

    (-9 | 6 | -3 18 | -12 | 6 -9 | 6 | -3)

    Trace

    -24

    Determinant

    0

    Matrix rank

    1

    Nullity

    2

    Characteristic polynomial

    -λ^3 - 24 λ^2

    Eigenvalues

    λ_1 = -24

    λ_2 = 0

    λ_3 = 0

    Eigenvectors

    v_1 = (3, -2, 1)

    v_2 = (-1, 0, 1)

    v_3 = (2, 1, 0)

    Diagonalization

    (-9 | 18 | -9 6 | -12 | 6 -3 | 6 | -3) = P.D.P^(-1) where P = (3 | -1 | 2 -2 | 0 | 1 1 | 1 | 0) D = (-24 | 0 | 0 0 | 0 | 0 0 | 0 | 0) P^(-1) = 1/8(1 | -2 | 1 -1 | 2 | 7 2 | 4 | 2)

    Condition number

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