If $A = \begin{bmatrix} \ 2 & 2 & 1 \\ \ 1 & 3 & 1 \\ \ 1& 2 & 2 \\ \end{bmatrix}$ , find the eigen values & eigen vectors of $A^3 +I$ .

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written 6.4 years ago by

teamques10 ★ 65k

modified 18 months ago by

sagarkolekar ★ 11k

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written 6.3 years ago by

teamques10 ★ 65k

• modified 6.1 years ago

To find eigen values & eigen vectors $A^3 +I$ first we find eigen values & eigen vectors of A Characteristic eqation is |A- λI| =0

i.e. $$ \begin{vmatrix} 2-λ&2&1 \\ 1&3-λ&1 \\ 1&2&2-λ \end{vmatrix} = 0 $$

Expanding we get a cubic equation in λ as $λ^3 - 7λ^2 + …

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