1 Problem 3.4. Consider the following plane with the both the red and black coordinate systems. The red axes correspond with what are normally thought of as the lines y and y = 4z. Let the two red vec- tors highlighted along the red axis be the basis vectors for a new "red basis", called r -{[3][4]} Cilli-Turner Spring 2017 23 Matrix Algebra Notes 1. Write the coordinates of each of the above points relative to both the red basis r and the black basis b 2. Determine a matrix that will: i. Rename points from the red basis as points in the black one. ii. Rename points from the black basis as points in the red one. 3. Consider now the transformation 7: R2R such that a stretch factor of 2 corresponds to the line y = and a stretch factor of -1 corresponds to the line y=4x. 4. Determine what happens to the vector [5]under this transformation and represent the answer according to the black basis. Explain all steps in your solution. 5. Determine what happens to the vector [5]=[33] under this transformation and represent the answer according to the red basis. Explain all steps in your solution. 6. Consider the following diagram, where y is the image of z under the transformation T, the matrices A and D are the stretch matrices in black and red respectively, and P renames vectors from red to black: [x]a 이 A[x] = [y]a [x], D[x] = [y]r D Find the matrices A, D, and P that correspond to this diagram for this particular problem.