Question

Use elementary column operation C₂ → C₂ + 2C₁ in the following matrix equation :

$\left(\begin{array}{cc}2& 1\\ 2& 0\end{array}\right)=\left(\begin{array}{cc}3& 1\\ 2& 0\end{array}\right)\left(\begin{array}{cc}1& 0\\ -1& 1\end{array}\right)$

Answer 1

$\left(\begin{array}{cc}2& 1\\ 2& 0\end{array}\right)=\left(\begin{array}{cc}3& 1\\ 2& 0\end{array}\right)\left(\begin{array}{cc}1& 0\\ -1& 1\end{array}\right)$

Applying C₂ → C₂ + 2C₁, we get

$\left(\begin{array}{cc}2& 5\\ 2& 4\end{array}\right)=\left(\begin{array}{cc}3& 1\\ 2& 0\end{array}\right)\left(\begin{array}{cc}1& 2\\ -1& -1\end{array}\right)$