Problem 3. Consider a 2 imes 2 matrix A that has an eigenvector [[2],[1]] with associated eigenvalue -3 , and an eigenvector [[-1],[1]] with associated eigenvalue of 9 . Determine the image of the vector vec(x)=[[1],[2]] under A in the following two ways:
(a) Express vec(x) as a linear combination of [[1],[2]],[[-1],[1]] and use your knowledge of eigenvalues.
(b) Calculate the matrix A and directly find Avec(x).
Problem 3.Consider a 2 2 matrix A that has an eigenvector
with associated eigen
value -3, and an eigenvector
with associated eigenvalue of 9. Determine the
image of the vector
1 under A in the following two ways: 2
(a Express x as a linear combination of
and use your knowledge of eigen-
values.
b) Calculate the matrix A and directly find Ax