On usign elementry column operation `C_(2)rArrC_(2)-2C_(1)` in the following matrix equation `[{:(1,-3),(2,4):}]=[{:(1,01),(0,1):}][{:(3,1),(2,4):}]` , we have

Options

A. `[{:(1,-5),(0,4):}]=[{:(1,-1),(-2,2):}][{:(3,-5),(2,0):}]`
B. `[{:(1,-5),(0,4):}]=[{:(1,-1),(0,1):}][{:(3,-5),(-0,2):}]`
C. `[{:(1,-5),(2,0):}]=[{:(1,-3),(0,1):}][{:(3,1),(2,4):}]`
D. `[{:(1,-5),(2,0):}] =[{:(1,-1),(0,1):}][{:(3,-5),(2,0):}]`

Explanation

To solve the matrix equation given the elementary column operation \( C_2 \rightarrow C_2 - 2C_1 \), we will perform the operation step by step on both the left-hand side (LHS) and the right-hand side (RHS) of the equation.

### Given Matrix Equation:
\[
\begin{bmatrix}
1 & -3 \\
2 & 4
\end{bmatrix}
...