Transformation Matrix Mystery?

📌 CONCEPT: A transformation matrix is a matrix that, when multiplied by a vector, transforms the vector according to a specific operation, in this case, enlargement of a photograph.

📐 RULE / FORMULA: The transformation matrix for enlargement of a photograph by factors a and b in the x and y directions, respectively, is given by the diagonal matrix

[ [a, 0], [0, b] ].

💡 WORKED EXAMPLE: Suppose the original size of the photograph is represented as the 2x2 matrix P = [ [2, 0], [0, 3] ] and we want to enlarge it by a factor of 3 in the x-direction and by a factor of 4 in the y-direction. Then, the transformation matrix is T = [ [3, 0], [0, 4] ] and the enlarged photograph is represented by the matrix PT = [ [6, 0], [0, 12] ].

⚠️ COMMON MISTAKE: Students may forget to use the correct factors for enlargement or incorrectly apply the transformation matrix, leading to incorrect results.