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    Cofactor

    Result

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

    Dimensions

    3 (rows) × 3 (columns)

    Matrix plot

    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) = S.J.S^(-1) where S = (3 | -1 | 2 -2 | 0 | 1 1 | 1 | 0) J = (-24 | 0 | 0 0 | 0 | 0 0 | 0 | 0) S^(-1) = (1/8 | -1/4 | 1/8 -1/8 | 1/4 | 7/8 1/4 | 1/2 | 1/4)

    Condition number

    ∞

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