Determine the Eigen Values and corresponding Eigen Vectors for the mat | Numerical Methods 2078

Numerical Methods20785 marksNumerical: Eigenvalues and eigenvectorsComputing eigenvalues and eigenvectors

Determine the Eigen Values and corresponding Eigen Vectors for the matrix.

$A = \begin{bmatrix} 1 & 6 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$

[5]

Determine the Eigen Values and corresponding Eigen Vectors for the matrix.

$$A = \begin{bmatrix} 1 & 6 & 1 \ 1 & 2 & 0 \ 0 & 0 & 3 \end{bmatrix}$$

[5]

$A = \begin{bmatrix} 1 & 6 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$ --- $\det(A - \lambda I) = 0$ $A - \lambda I = \begin{bmatrix} 1-\lambda & 6 & 1 \\ 1 & 2-\lambda & 0 \\ 0 & 0 & 3-\lambda \end{bmatrix}$ Expand along Row 3 (only one nonzero entry $3-\lambda$ ): $$\det = (3-\lambda)\lef...

$$A = \begin{bmatrix} 1 & 6 & 1 \ 1 & 2 & 0 \ 0 & 0 & 3 \end{bmatrix}$$ --- $$\det(A - \lambda I) = 0$$ $$A - \lambda I = \begin{bmatrix} 1-\lambda & 6 & 1 \ 1 & 2-\lambda & 0 \ 0 & 0 & 3-\lambda \end{bmatrix}$$ Expand along Row 3 (only one nonzero entry $3-\lambda$): $$\det = (3-\lambda)\lef...

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