Module 5: Linear Systems and Functional Approximation Questions Question 1 Solve the equation Ax=b for x by calculating an LU decomposition of A and back (2 1 1 solving, where A=( 0 1 0 and be} } 2 3 Question 2 ( Find the best least squares solution to the matrix equation Ax=b. (3 Question 3 Prove that if matrix A has an eigenvalue 2 then matrix AK (the kth power of A) has an eigenvalue 2k. Question 4 Compute a QR factorization of the matrix 6 16 8 18 Question 5 Compute the LU factorization of the matrix 1 1 3 A = 1 4 2 5 (That is, fid [ and U with A = LU.)