Question

In the following matrix equation use elementary operation R₂ → R₂ + R₁ and the equation thus obtained:

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

Answer 1

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

By applying elementary operation R₂ → R₂ + R₁, we get

\[\begin{bmatrix}2 & 3 \\ 3 & 7\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 17 & - 7\end{bmatrix}\]
(Every row operation is equivalent to left-multiplication by an elementary matrix.)