Use the indicated row operation to change the matrix.
-Replace $ R_{2} $ by $ \frac{1}{3} R_{1}+\frac{1}{2} R_{2} $.
$ \left[\begin{array}{rr|r}3 & 0 & 15 \ -2 & 4 & 12\end{array}\right] $
A) $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 0 & 2 & 11\end{array}\right] $
B) $ \left[\begin{array}{rr|r}3 & 0 & 15 \ -1 & 2 & 6\end{array}\right] $
C) $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 1 & 4 & 27\end{array}\right] $
D) $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 0 & 0 & 11\end{array}\right] $

Question

Quizplus · Accepted Answer

To find the new $ R_2 $, we apply the operation $ \frac{1}{3} R_{1}+\frac{1}{2} R_{2} $:- For the first column: $ \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (-2) = 1 - 1 = 0 $- For the second column: $ \frac{1}{3} \cdot 0 + \frac{1}{2} \cdot 4 = 0 + 2 = 2 $- For the right side of the equation: $ \frac{1}{3} \cdot 15 + \frac{1}{2} \cdot 12 = 5 + 6 = 11 $Thus, the new matrix is $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 0 & 2 & 11\end{array}\right] $.

Use the Indicated Row Operation to Change the Matrix R2 R_{2} R2​

Use the Indicated Row Operation to Change the Matrix $R_{2}$