# Argument matrix row operations (3x4)

Background

Given the argument matrix

$$A=\begin{bmatrix}1 & 3 & -5 & 3\\4 & 10 & -6 & -4\\-4 & -14 & -4 & -5\end{bmatrix}$$

perform each row operation in the order specified and enter the final result.

My work so far

a) First: $$R2→R2-4R1$$

$$\begin{bmatrix}0 & -2 & 14 & -16\end{bmatrix}$$

b) Second: $$R3→R3+4R1$$

$$\begin{bmatrix}0 & -2 & -24 & 7\end{bmatrix}$$

Am I on the right track here? I'm using RREF to work these out.

• what is the "order specified"? – Exodd Jul 6 at 20:47
• What exactly is your aim here? I am not sure. – Carlo Jul 6 at 22:16
• It's written above. Solve first for R2→R2−4R1, then second, R3→R3+4R1. – Laufen Jul 6 at 22:18

You're on exactly the right track! The only thing is when you do a row (column) operation, that row isn't isolated, it becomes that row (column) in the new matrix. That is, $$R_2 \rightarrow R_2 - 4R_1$$ gives $$\begin{bmatrix} 1 & 3 & -5 & 3 \\ 0 & -2 & 14 & -4 \\ -4 & -14 & -4 & -5 \end{bmatrix}.$$ Then, when you perform the next operation, the same thing happens with the next row. That is $$R_3 \rightarrow R_3 + 4R_1$$ gives $$\begin{bmatrix} 1 & 3 & -5 & 3 \\ 0 & -2 & 14 & -4 \\ 0 & -2 & -24 & 7 \end{bmatrix}.$$ Keep up the good work!