## Find a Row-Equivalent Matrix which is in Reduced Row Echelon Form and Determine the Rank

## Problem 643

For each of the following matrices, find a row-equivalent matrix which is in reduced row echelon form. Then determine the rank of each matrix.

**(a) **$A = \begin{bmatrix} 1 & 3 \\ -2 & 2 \end{bmatrix}$.

**(b)** $B = \begin{bmatrix} 2 & 6 & -2 \\ 3 & -2 & 8 \end{bmatrix}$.

**(c)** $C = \begin{bmatrix} 2 & -2 & 4 \\ 4 & 1 & -2 \\ 6 & -1 & 2 \end{bmatrix}$.

**(d)** $D = \begin{bmatrix} -2 \\ 3 \\ 1 \end{bmatrix}$.

**(e)** $E = \begin{bmatrix} -2 & 3 & 1 \end{bmatrix}$.