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Linear Algebra

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Reducing Matrices

LINALG-MDNGEW

Let $M$ be the matrix:

$$M = \left[ \begin{matrix} 2 & 3 \\\ 3 & 2 \end{matrix} \right]$$

Which of the following would reduce $M$ to echelon form (not necessarily reduced echelon form)?

A

Scale row $2$ by the scalar $2$, then subtract row $1$ from row $2$.

B

Subtract row $1$ from row $2$, then subtract $2$ times row $2$ from row $1$.

C

Scale row $2$ by the scalar $3$, then swap rows $1$ and $2$.

D

Scale row $2$ by the scalar $2$, then subtract $3$ times row $1$ from row $2$.

E

Scale row $1$ by $3$, scale row $2$ by $2$, and swap.