Linear Algebra questions and answers in November 2022

. Describe all least-squares solutions of the equation Ax = b. 101 1 10 3 1 0 1 17 A= b= 1 10 4 1 10 2 101 6 The least-squares solutions are all vectors of the form x = + Xq with Xz free. (Simplify ...

. (1 point) A furniture company makes bar stools, tables, and chairs. Each bar stool requires 1 hour of labor, 8 feet of wood, and 0.2 gallons of stain. Each chair requires 4 hours of labor, 16 feet...

. Let O A = 0 0 8 (a) Find AT A and AA and the singular vectors v1, V2, u1, u2 for the matrix A. (b) Check that Avi = oui and Av2 = 02U2. (c) Check that A = ouiV1 + 02u2V2 . (d) Let B be the matrix ...

Burdell Distilleries in Knoxville is opening a new facility for its whiskey production. There are 3 machines, a, b, and c. Machine a uses 6 pounds of corn, 18 pounds of barley and 6 pounds of rye to p...

. 5. [HAND IN 12 marks] In the diagram below, the 2x2 shaded square centred at the origin is bounded by the lines x = +1 and y = +1. Let T denote the linear transformation that maps the square on th...

. 4.(5 marks) Consider the system of equations: AB = W Here B is the vector on unknowns. To have some common notation, let the columns of A be u and v. Suppose we are given that the least-squares ap...