You can ignore the matlab questions / do not need matlab

Consider matrix A: N - 1 -2 A = O 1 -2 O -2 (a) Find all 3 eigenvalues of matrix A. Show work. Stipulation: To show work, you must list all algebraic steps (ie. Factoring polynomials) that lead towards the 3 eigenvalues of A. (b) Now, immediately use the eig function to check your work. Add this to your matlab script, and echo the eigenvalues and eigenvectors for matrix A in the main command window (we will grade the echoed outputs from your published PDF file). (c) Find all 3 eigenspaces of matrix A. Show work (Note: You should be able to evaluate the determinant by hand without using matlab's roots function) Stipulation: To show work, you must set up the necessary nullspace equations (A - An! ) v = 0, and also, write out all the row reduction steps that lead towards the answers for each eigenvector of A. (d) Now, you can actually check your row-reduction work in matlab !! In your matlab script, add the 3 following commands and echo the answers for each. Ideally, if your math in (c) were all correct, the RREF answers from these 3 commands will help you verify the correct "free column" positions for your work in (c). rref_work for vlA rref (A - D (1, 1) *eye (3) ) These 3 commands are equivalent to this rref_work for_v2A = rref (A - D (2, 2) *eye (3) ) expression: rref_work_for v3A = rref (A - D (3, 3) *eye (3) ) rref ( A - an 1) where "D" = the eigenvalue matrix from your eig command: [V, D] = eig (A)(e) Compare your hand-derived eigenvectors versus the answer from the eig command: From the eig command Hand-derived eigenvectors (or eigenspaces) 0.xxxx 0.xxxx V OOH .xxxx 0. xxxx V , = S . . vz = = [: ] .