Geometric Transformations

Finding a Matrix--Solutions

The problem (posed on page 31): find the matrices which perform the transformations pictured below.
Method 1: Use matrix forms already given (page 28) to determine elements of the transformation matrix. For a) we can see that we need a scale matrix. We need to scale along the y-axis; in particular we need y = 1.5 to become y = 3, and y =2.5 to become y = 5. The x values do not change. So the matrix would be
Method 2: Solve linear equations to find the matrix coefficients. We know that in general

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