Question

problem 3. (12 points)
perform the row operation $2r_1 + r_2 \
ightarrow r_2$ on the matrix below.
$\left\

$$\begin{array}{cc|c}1 & 6 & -6\\\\-2 & 6 & -3\\end{array}$$

\
ight \stackrel{2r_1 + r_2 \
ightarrow r_2}{\longrightarrow} \left\

$$\begin{array}{cc|c}\\square & \\square & \\square\\\\\\square & \\square & \\square\\end{array}$$

\
ight$
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Explanation:

Step1: Identify Row 1 and Row 2

Row 1 ($R_1$): $[1, 6, -6]$, Row 2 ($R_2$): $[-2, 6, -3]$

Step2: Apply $2R_1 + R_2$ to Row 2

First element: $2(1) + (-2) = 0$
Second element: $2(6) + 6 = 18$
Third element: $2(-6) + (-3) = -15$
Row 1 remains unchanged: $[1, 6, -6]$

Answer:

$$\begin{bmatrix} 1 & 6 &\bigm\vert& -6 \\ 0 & 18 &\bigm\vert& -15 \end{bmatrix}$$