Matrix Transformation Puzzle?

📌 CONCEPT: A matrix transformation is a linear transformation represented by a matrix that changes the position of a point in a plane, preserving the straight lines and angles.

📐 RULE / FORMULA: The effect of applying a matrix transformation T to a point (a, b) is given by the transformation matrix multiplied by the column vector representing the point.

💡 WORKED EXAMPLE: Let's apply the transformation T to the point (a, b) using the given matrix. The transformation matrix is

[ 1 -3 4 2 ]

To find the new coordinates (x', y'), we multiply the transformation matrix with the column vector [a, b]' and get:

x' = 1*a -3*b + 0*y'

y' = 4*a + 2*b + 0*y'

Thus, the new coordinates (x', y') are (a -3b, 4a + 2b).

⚠️ COMMON MISTAKE: Students often forget to multiply the transformation matrix with the column vector representing the point, leading to incorrect results.