Chapter 2.5, Problem 22E

(Reduced LU Factorization) With A as in the Practice Problem, find a 5 × 3 matrix B and a 3 × 4 matrix C such that A = BC. Generalize this idea to the case where A is m × n. A = LU, and U has only three nonzero rows.

Find an LU factorization of $A=\left[\begin{array}{cccc}2& -4& -2& 3\\ 6& -9& -5& 8\\ 2& -7& -3& 9\\ 4& -2& -2& -1\\ -6& 3& 3& 4\end{array}\right]$.[Note: It will turn out that A has only three pivot columns, so the method of Example 2 will produce only the first three columns of L. The remaining two columns of L. come from I₅.]