Ignore matlab questions

Problem 4: When you have a "zero eigenvalue\" Consider matrix E: 752 E1 572 -6 _ _ 22Ar (a) Open the matlab script {you don't have to turn onhing in for Part (a) we're jus setting some stuff up !) Problem4_eigenvalue_transformat ions . m Copyr the entire script onto your own matlab script { EKl 03_ps7_outputs .m) . Then, change the pre- existing matrix E to the E you see above. Run the entire code, and you'll see the eigenvalues and eigenvectors of E echoed in the command window. Furthermore, you'll see a plot containing the following: (i) A semi-transparent pink unit sphere (prior to transformation E), and then, (ii) A blue disc that represents the post-transformed image of the sphere by transformation E (iii) 3 lines that represent the eigenvectors of E 1 Now, examine the eigenvalues and eigenvectors of E. Notice the eigenvector 171 = I 1' associated with the 1 zero-eigenvalue ill 2 0 appears to be somewhat perpendicular to the flattened blue disc, whereas the other 2 eigenvectors E and FE; seem to lie flat on the blue disc. (b) In 1 or 2 sentences, describe the "3D transformation action" of the eigenvalue-eigenvector pair 11 = 0 and Hint: The answer we are looking for can be seen in this video. https://www.youtube.com/watch?v=AOBYDupxmtA (c) Are v1 , V2 , and v3 a set of linearly-independent eigenvectors ? First, justify your answers just by looking at the geometrical orientations of the 3 vectors shown in your current matlab plot. Then, justify your answer by using Theorem 2 in Lay, Ch. 5.1. (d) Suppose I claim that the eigenvector v1 = associated with the zero-eigenvalue 11 = 0 resides within the nullspace of E . The question is: Am I right ???? =\\ You Task: Plug in 21 = 0 into the nullspace equation ( E - 1 1) v1 = 0. Then, show that you end up with the equation E v1 = 0. Finally, using 1 or 2 sentences, give me a mathematical reason on why E v1 = 0 either supports my claim... or rejects my claim ! (e) Now, look at your 3D plot again. It seems like eigenvectors v2 and 13 are both perpendicular to , , right? Prove it by performing the matrix product in your matlab script, echo the answer in your command window: VT V In 1 or 2 sentences (in terms of dot products), tell me why V V can be used to prove that 2 and 13 are both perpendicular to v1(f) Using the geometrical information you've gathered from parts (d) and (e), complete the following sentence: For our symmetric matrix E , vector v, lies within the of A, whereas vectors v2 and V3 both lie within the of E. The 4 possible answers for both blank spaces are: N(E) nullspace , C(E) column space , R(E) row space, N(ET) left nullspace (g) Finally: Publish your matlab script EK103 ps7 outputs.m as a PDF file, and attach it to your hand- written work PDF for submission