2. Writing Eigenvector Examples Using random matrices for practicing eigenvector and eigenvalue questions will often result in non-integer values that are confusing and tedious to calculate. Use the following to reverse engineer a question. i. Give three simple, linearly independent column vectors x1,x2,X3 E 1R3. Ensure that they each have at least 2 non-zero entries, and that one of your values is negative. {these are your ei genvectors] ii. Pick three eigenvalues, A1,A2,A3. Use integer values, and have one of your A5, such that Ag {C 0. iii. We know that Ax = Ax for each of your eigenvectors. Hence set up a system AX = B where X = [K1X2X3] is the matrix with your eigenvectors as columns, and solve for A. 5 marks