Exercises

01

Back substitution: convert REF to RREF

Convert $\left(\begin{array}{rrrrrr}1& -3& 0& -1& 0& -2\\ 0& 2& 0& 0& -8& 2\\ 0& 0& 0& 1& 9& 4\\ 0& 0& 0& 0& 0& 0\end{array}\right)$ from REF to RREF.

02

Comparing elimination and elimination

Explain (with some details in an example) how elimination for matrices (corresponding to multiplication by $L_i^{-1}$ for some single-column row-add combo matrix $L_i^{-1}$) is equivalent to elimination for a system of equations.

Hint: solve the above system using elimination and back substitution as in high school algebra, and then solve the same system as a vector preimage problem using row reduction to RREF of the augmented matrix. Write your solution steps in corresponding order so that you can match the corresponding steps between the two methods.