# Solve $Lx = b$ for $x$ when $b = (1, 1, 2)^T$.

Let $L$ be a $3×3$ symmetric matrix with eigenvalues $?_1 = ?1$, $?_2 = ?2$, and $?_3 = ?3$ and their corresponding egenvectors $v_1 = (1, 1, 1)^T$, $v_2 = (2, ?1, ?1)^T$, and $v_3 = (0, 1, ?1)^T$ where $T$ denotes the transpose.

Solve $Lx = b$ for $x$ when $b = (1, 1, 2)^T$.

Note: this is the idea behind Sturm-Liouville series solutions of ODE boundary value problems.

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