Matrix Factorization

Exercise2-7

Exercise2-7

1. Solve the following linear system

$\left(\begin{array}{rrr} 1 &0&0\\ 2&1&0\\ -1&0&1 \end{array}\right)\left(... ...\end{array}\right) = \left(\begin{array}{r} 2\\ -1\\ 1 \end{array}\right)$

2. Factor the following matrices into the $LU$ decomposition.

(a) $\left(\begin{array}{rrr} 2&-1&1\\ 3&3&9\\ 3&3&5 \end{array}\right)$

(b) $\left(\begin{array}{rrrr} 2&0&0&0\\ 1&1.5&0&0\\ 0&-3&0.5&0\\ 2&-2&1&1 \end{array}\right)$