(10 points) Suppose A E Rnxn and r E R" are given. Give an efficient algorithm for computing the first column of M = (A-x1I)(A-$2I) . . . (A-EnI). What is the number of floating-point operations of your algorithm? (You only need to give the leading term as n tends to co.) (15 points) If u and v are in R", then the matrix A = I + uv is called a rank-one perturbation to the(10 points) Suppose A E Rnxn and r E R" are given. Give an efficient algorithm for computing the first column of M = (A-x1I)(A-$2I) . . . (A-EnI). What is the number of floating-point operations of your algorithm? (You only need to give the leading term as n tends to co.) (15 points) If u and v are in R", then the matrix A = I + uv is called a rank-one perturbation to the