

1. Formulate the following problem as least squares problems. For each problem, give a matrix A and a vector b such that the problem can be expressed as argmin |lAx - bllz (you are not asked to solve...
Formulate the following problems as least-squares problems. For each problem, give a matrix A and a vector b, such that the problem can be expressed as minimize IAx-bi (You do not have to solve the problems.) (a) Minimize x1+ 2x + 3x[+ (x,-x2 + x3-1)2 + (-ri-4x2 + 2)2. (b) Minimize (-6r2 4)43r228r2-3)2 (e) Minimize 2(-6x2+ 4)2 + 3(-4x1 +3x2-1尸+4(x1 + 8x2-3)2. 1+(-i - 4r2 +2)2
Formulate the following problems as least-squares problems. For each problem, give a matrix A...
Formulate the following problems as linear programs. (a) Minimize llAr-blli subject to ll a) Minimize |A 1. (b) Minimize llal|1 subject to llAr -bllo 1. (c) Minimize |A-o In each problem, assume A Rixn and b E R" are given
Formulate the following problems as linear programs. (a) Minimize llAr-blli subject to ll a) Minimize |A 1. (b) Minimize llal|1 subject to llAr -bllo 1. (c) Minimize |A-o In each problem, assume A Rixn and b E R" are given
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...