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Introduction to Linear Algebra

Exercise 2.7.24

Answers

The condition $PA = LU$ means

[\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}] [\begin{matrix} 0 & 1 & 2 \\ 0 & 3 & 8 \\ 2 & 1 & 1 \end{matrix}] = [\begin{matrix} 1 \\ 0 & 1 \\ 0 & 1 ∕ 3 & 1 \end{matrix}] [\begin{matrix} 2 & 1 & 1 \\ 3 & 8 \\ - 2 ∕ 3 \end{matrix}] .

If we wait to exchange and $a_{12}$ is the pivot,

A = L_{1} P_{1} U_{1} = [\begin{matrix} 1 \\ 3 & 1 \\ 1 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ 1 & 1 \end{matrix}] [\begin{matrix} 2 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 2 \end{matrix}] .

mathchakra

2022-01-16 12:35

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