Graded Assigment Issue in problem 5 (Eigenvalues and Eigenvectors)

I am unable to solve this question

Question 5

Select the eigenvectors, using the eigenvalues you found for the above matrix A⋅B in Q4.

I get the answer as (1,0) & (0,1) however none of the options are matching. The Eigen values are 4,1. Or I need help in solving this.

Hi @Anil_K1!

Remember that you must solve the following. For the eigenvalue \lambda = 4, an eigenvector must satistfy

\begin{bmatrix} 1 & 2 \\ 0 & 4 \end{bmatrix} \left(\begin{array}{c} x \\ y \end{array}\right) = 4 \cdot \left(\begin{array}{c} x \\ y \end{array}\right)

This must be translated to a 2 \times 2 linear system. Then you must solve it for x and y. The values for x and y, in the form (x,y) is the vector you are looking for.

I hope that helps.