WAEC - Further Mathematics (2023 - No. 31)
A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)
\(\begin{bmatrix} 4&0\\1&4\end{bmatrix}\)
\(\begin{bmatrix} 4&4\\0&0\end{bmatrix}\)
\(\begin{bmatrix} 4&0\\0&4\end{bmatrix}\)
\(\begin{bmatrix} 4&1\\0&4\end{bmatrix}\)
설명
\(P : (x, y) → (2x + y, -2y)\)
\(p\begin{bmatrix} x\\y\end{bmatrix}=\begin{bmatrix} 2x & y\\0 &-2y\end{bmatrix}\)
\(\therefore p = \begin{bmatrix} 2 & 1\\0 &-2\end{bmatrix}\)
\(\therefore p^2 = \begin{bmatrix} 2&1\\0&-2\end{bmatrix}\) \(\begin{bmatrix} 2&1\\0&-2\end{bmatrix}\) = \(\begin{bmatrix} 4&0\\0&4\end{bmatrix}\)