4. Let A e Rmxn (a) Show that N(ATA) = N(A). That is, the null space of A can be determined by computing eigenvectors correspond- ing to the zero eigenvalue for ATA. (b) Let A E where c E R. Compute eigenvalues for the matrix AA by hand. For which values of the null-space of A is trivial? (c) Determine N(A) using matlab, when e = 1, 10- and 10-9. Compute eigenvalues and corresponding eigenvectors for A"A numerically. Does Matlab agree with you on the dimension of N(A) for each value of e? Include the script that you used and the computed eigenvalues and vectors to your solution. Hints: (a) The inclusion N(A) C N(AT A) can be easily proven. To prove that N(AT A) C N(A), multiply A'A from both sides with a and interpret the result as || Ax?. (c) Try out the commands help eig and format long in Matlab