Questions

01

Order doesn’t matter when multiplying row-add matrices of the same column

Explain why (or prove algebraically that) order does not matter when multiplying row-add matrices with their nonzero subdiagonal entries lying in the same column. Explain this in general, not just for the $4\times 4$ matrix above.

02

Compute LU factorization

Find the LU factorization of the matrix $A=\left(\begin{array}{rrr}7& 1& 1\\ -28& 0& 5\\ 14& 14& 31\end{array}\right)$.