Matrix decompositions

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Gaussian elimination writes $A = LU$ with unit lower-triangular $L = \begin{pmatrix} 1 & 0 \\ m & 1 \end{pmatrix}$. For $A = \begin{pmatrix} -2 & -4 \\ -8 & -1 \end{pmatrix}$, find the multiplier $m$ used to eliminate the $(2,1)$ entry (row2 $\to$ row2 $- m\cdot$row1).

2. Warm-up

   Gaussian elimination writes $A = LU$ with unit lower-triangular $L = \begin{pmatrix} 1 & 0 \\ m & 1 \end{pmatrix}$. For $A = \begin{pmatrix} 5 & 4 \\ 15 & 3 \end{pmatrix}$, find the multiplier $m$ used to eliminate the $(2,1)$ entry (row2 $\to$ row2 $- m\cdot$row1).

3. Warm-up

   Gaussian elimination writes $A = LU$ with unit lower-triangular $L = \begin{pmatrix} 1 & 0 \\ m & 1 \end{pmatrix}$. For $A = \begin{pmatrix} -4 & 1 \\ 16 & -2 \end{pmatrix}$, find the multiplier $m$ used to eliminate the $(2,1)$ entry (row2 $\to$ row2 $- m\cdot$row1).

Problems shown under their original terms: Generated (template, solver-computed).