A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.

  • A (7, -2)
  • B (5, -2)
  • C (-2, 7)
  • D (-7, 2)
waec 2022furthermathematics

The correct answer is A. (7, -2)

Let (x1, y1) be the image of the point (x, y) under the given transformations.

x1 = 3x - y

y1 = x + 4y

\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} x \\ y = \end{vmatrix}  \begin{vmatrix} x_1 \\ y_1 \end{vmatrix}\)

\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} 2 \\ 1 = \end{vmatrix}  \begin{vmatrix} 7 \\ -2 \end{vmatrix}\)

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