normally an element x of is written as (x,y) (sometimes as ). so for the example here:
you can check your answer by multiplying your two matrices together, and verifying you get the 2x2 identity matrix.
Consider the linear transformation, , for which is found by rotating the point x through an angle of anticlockwise about the origin.
a) Find the 2 x 2 matrix A for which T(x) = Ax
I wasn't quite sure how could = Ax and as such I wasn't entirely sure how to answer the question. I just applied the same method I had been using for all the previous question to get:
Is this the correct answer for matrix A? I thought this would be ? What is the x value that A is multiplied by?
b) Write down the transformation that returns the point x to its original position.
Since we rotated everything counter-clockwise, I would presume that to reverse that transformation we would rotate everything by to get:
Is this correct?