Question

If $A=\left[\begin{array}{ccc}1& 0& 2\\ 2& 3& 4\end{array}\right]$, apply the transformation $C_1\to C_1+2C_3$.

Answer 1

$A=\left[\begin{array}{ccc}1& 0& 2\\ 2& 3& 4\end{array}\right]$

Applying $C_1\to C_1+2C_3$, we have

$A=\left[\begin{array}{ccc}(1+2\times 2)& 0& 2\\ (2+2\times 4)& 3& 4\end{array}\right]$

$A=\left[\begin{array}{ccc}5& 0& 2\\ 10& 3& 4\end{array}\right]$