Matrix Transformations
Muhtasari
Every 2 by 2 matrix secretly describes a way of moving every point in the plane at once: multiply a point's coordinates by the matrix and out comes its image after a reflection, a rotation, an enlargement, or a shear. Recognising which matrix produces which transformation, and combining several transformations into a single matrix, turns geometry into pure algebra.
This topic builds directly on matrix multiplication: you will meet the standard matrices for reflections in the coordinate axes and the lines y = x and y = -x, rotations about the origin, enlargements centred at the origin, and shears, then combine transformations by multiplying their matrices together.
Malengo
- Understand transformations of the plane associated with 2 x 2 matrices, including reflections, rotations about the origin and enlargements with centre at the origin
- Find and use combination of transformations using matrix multiplication
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- Which matrix represents a reflection in the y-axis? A) [[1,0],[0,-1]] B) [[-1,0],[0,1]] C) [[0,1],[1,0]] D) [[-1,0],[0,-1]] Answer: B
- Which matrix represents a 90 degree anticlockwise rotation about the origin? A) [[0,1],[-1,0]] B) [[0,-1],[1,0]] C) [[-1,0],[0,-1]] D) [[1,0],[0,1]] Answer: B
- The matrix [[4,0],[0,4]] represents: A) a rotation of 90 degrees B) a reflection in the x-axis C) an enlargement, scale factor 4, centre the origin D) a shear Answer: C
- If R is carried out first, followed by M, the matrix for the combined transformation is: A) RM B) MR C) R + M D) M - R Answer: B
- A matrix that represents a shear parallel to the x-axis has the form: A) [[1,0],[k,1]] B) [[1,k],[0,1]] C) [[k,0],[0,k]] D) [[0,1],[1,0]] Answer: B
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