The matrix $$ B $$ below is the result of performing a single row operation on the matrix $$ A $$. Identily the row operation. $$ A=\left[\begin{array}{ll|l}2 & 3 & 5 \ 4 & 6 & 8\end{array} ight] \quad B=\left[\begin{array}{ll|l}2 & 3 & 5 \ 2 & 3 & 4\end{array} ight] $$ What row operation will convert the first augmented matrix into the second augmented matrix? A. $$ R_{2}-R_{1} ightarrow R_{2} $$ B. $$ 2 R_{2} ightarrow R_{2} $$ C. $$ \frac{1}{2} R_{2} ightarrow R_{2} $$ D. $$ R_{2}+R_{1} ightarrow R_{2} $$

Question

The matrix $$ B $$ below is the result of performing a single row operation on the matrix $$ A $$. Identily the row operation. $$ A=\left[\begin{array}{ll|l}2 & 3 & 5 \ 4 & 6 & 8\end{array}ight] \quad B=\left[\begin{array}{ll|l}2 & 3 & 5 \ 2 & 3 & 4\end{array}ight] $$ What row operation will convert the first augmented matrix into the second augmented matrix? A. $$ R_{2}-R_{1} ightarrow R_{2} $$ B. $$ 2 R_{2} ightarrow R_{2} $$ C. $$ \frac{1}{2} R_{2} ightarrow R_{2} $$ D. $$ R_{2}+R_{1} ightarrow R_{2} $$

UpStudy AI · Accepted Answer

To determine the row operation that transforms matrix $$ A $$ into matrix $$ B $$, let's analyze the changes between the two matrices.

**Matrix $$ A $$:**
$$
\begin{bmatrix}
2 & 3 & | & 5 \
4 & 6 & | & 8 \
\end{bmatrix}
$$

**Matrix $$ B $$:**
$$
\begin{bmatrix}
2 & 3 & | & 5 \
2 & 3 & | & 4 \
\end{bmatrix}
$$

**Observations:**
- The **first row** remains unchanged.
- The **second row** changes from $$[4 \quad 6 \quad | \quad 8]$$ in matrix $$ A $$ to $$[2 \quad 3 \quad | \quad 4]$$ in matrix $$ B $$.

**Determining the Row Operation:**
To convert the second row of $$ A $$ to the second row of $$ B $$, observe the following calculation:
$$
\begin{align*}
[4 \quad 6 \quad | \quad 8] \times \frac{1}{2} &= \left[4 \times \frac{1}{2} \quad 6 \times \frac{1}{2} \quad | \quad 8 \times \frac{1}{2}\right] \
&= [2 \quad 3 \quad | \quad 4]
\end{align*}
$$
This operation involves scaling the second row by $$\frac{1}{2}$$.

**Conclusion:**
The row operation that achieves this transformation is:
$$
\frac{1}{2} R_2 \rightarrow R_2
$$

**Answer:**

C. $$ \frac{1}{2} R_{2} \rightarrow R_{2} $$
The row operation is $$ \frac{1}{2} R_{2} \rightarrow R_{2} $$.

The matrix below is the result of performing a single row operation on the matrix . Identily the row operation.

What row operation will convert the first augmented matrix into the second augmented matrix?
A.
B.
C.
D.

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The matrix below is the result of performing a single row operation on the matrix . Identily the row operation. What row operation will convert the first augmented matrix into the second augmented matrix? A. B. C. D.