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 ( R". Ensure that they each have at least 2 non-zero entries, and that one of your values is negative. (these are your eigenvectors) ii. Pick three eigenvalues, Aj, A2, A3. Use integer values, and have one of your A; such that MiCO. iii. We know that Ax = Ax for each of your eigenvectors. Hence set up a system AX = B where X = [x1x2x3] is the matrix with your cigenvectors as columns, and solve for 1. 5 marks