Math Snap

STEP 1

1. We are given a matrix and need to perform a specific elementary row operation.
2. The operation $\frac{1}{3} R_{2} \rightarrow R_{2}$ means to multiply every element in the second row by $\frac{1}{3}$.
3. The matrix is a $2 \times 3$ matrix, with the second row being $[-6, 9, 3]$.

STEP 2

1. Identify the elements in the second row.
2. Apply the row operation to each element in the second row.
3. Write the resulting matrix after the operation.

STEP 3

Identify the elements in the second row of the matrix:
The second row is $[-6, 9, 3]$.

STEP 4

Apply the row operation $\frac{1}{3} R_{2} \rightarrow R_{2}$ to each element in the second row:
- Multiply $-6$ by $\frac{1}{3}$:
$$ -6 \times \frac{1}{3} = -2
\] - Multiply $9$ by $\frac{1}{3}$:
$$ 9 \times \frac{1}{3} = 3
\] - Multiply $3$ by $\frac{1}{3}$:
$$ 3 \times \frac{1}{3} = 1
\]

Write the resulting matrix after performing the operation:
The first row remains unchanged: $[1, 3, 2]$.
The new second row is: $[-2, 3, 1]$.
Thus, the resulting matrix is:
$$\left[\begin{array}{cc:c} 1 & 3 & 2 \\ -2 & 3 & 1 \end{array}\right]$$ The resulting matrix is:
$$\left[\begin{array}{cc:c} 1 & 3 & 2 \\ -2 & 3 & 1 \end{array}\right]$$