A linear transformation T is defined by T: (x,y) → (3x – y, x + 4y). Find the image of (2, -1) under T.
-
(7, -2)
- (5, -2)
- (-2, 7)
- (-7, 2)
The correct answer is: A
Explanation
Let (x1, y1) be the image of the point (x, y) under the given transformations.
x1 = 3x - y
y1 = x + 4y
\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} x \\ y = \end{vmatrix} \begin{vmatrix} x_1 \\ y_1 \end{vmatrix}\)
\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} 2 \\ 1 = \end{vmatrix} \begin{vmatrix} 7 \\ -2 \end{vmatrix}\)