Repeat exercise assuming u and v are eigenvectors of a that

Question

Question: Repeat Exercise, assuming u and v are eigenvectors of A that correspond to eigenvalues 1 and 3, respectively.

Exercise: Let u and v be the vectors shown in the figure, and suppose u and v are eigenvectors of a 2 X 2 matrix A that correspond to eigenvalues 2 and 3, respectively. Let T : R² → R² be the linear transformation given by T (x) = Ax for each x in R², and let w = u + v. Make a copy of the figure, and on the same coordinate system, carefully plot the vectors T (u), T(.v), and T .(w).