Question

Use elementary column operation C₂ → C₂ + 2C₁ in the following matrix equation : \[\begin{bmatrix} 2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]

Answer 1

\[\begin{bmatrix}2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]

Applying C₂ → C₂ + 2C₁, we get

\[\begin{bmatrix}2 & 5 \\ 2 & 4\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 2 \\ - 1 & - 1\end{bmatrix}\]