Question

The operation $R_1 \rightarrow R_1 + R_2$ is applied on matrix $\begin{bmatrix} 2 & 3 \\ 6 & 4 \end{bmatrix}$, then which of the following will be resulting matrix?

• A. $\begin{bmatrix} 8 & 7 \\ 6 & -4 \end{bmatrix}$
• B. $\begin{bmatrix} 8 & 7 \\ 6 & 4 \end{bmatrix}$
• C. $\begin{bmatrix} 8 & 7 \\ 6 & 5 \end{bmatrix}$
• D. $\begin{bmatrix} 8 & 7 \\ 6 & 2 \end{bmatrix}$

Answer 1

Answer: (B)

$\begin{bmatrix} 8 & 7 \\ 6 & 4 \end{bmatrix}$

Answer 2

The elementary row operation $R_1 \rightarrow R_1 + R_2$ means we add the second row to the first row.

Given matrix: $\begin{bmatrix} 2 & 3 \\ 6 & 4 \end{bmatrix}$

Applying the operation:

New first row, first element: $2 + 6 = 8$ New first row, second element: $3 + 4 = 7$

The second row remains unchanged.

Resulting matrix: $\begin{bmatrix} 8 & 7 \\ 6 & 4 \end{bmatrix}$