maredia (ahm834) - Q11 - tegtmeyer - (54630) This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. 001 10.0 points Construct the normal equations for the least-squares solution of Ax = b when 1 2 2 A = 0 0 , b = 1 . 2 3 6 1. 2. 8 5 3. 5 8 \u0014 \u0015 6 x1 = x 2 2 13 8 \u0014 x1 x2 13 8 13 8 \u0015 = 14 22 10.0 points Find the least-squares solution of Ax = b when 1 0 6 A = 1 1 , b = 1 . 1 1 4 \u0015 \u0014 1 19 1. 2 12 \u0015 \u0014 1 12 2. 2 15 002 1 \u0015 \u0014 3 3. 3 \u0015 \u0014 6 8 x1 = x2 2 5 \u0014 \u0015 1 17 4. 2 7 \u0014 \u0015 6 5. 1 003 10.0 points A least-squares solution of Ax = b is a that satisfies vector x A x = projCol(A) b . 4. 1 0 2 2 2 \u0014 \u0015 x 0 1 = 1 x2 6 3 True or False? 1. TRUE 2. FALSE 5. 13 8 8 \u0014 x1 x2 5 \u0015 = 14 22 004 Find the Least Squares Regression line y = mx + b that best fits the data points (1, 1), 6. 1 0 2 2 6 \u0014 \u0015 x 0 1 = 2 x2 6 3 10.0 points 1. y = 2 x1 3 2. y = x + 2 3 (0, 2), (1, 1) . maredia (ahm834) - Q11 - tegtmeyer - (54630) 3. y = x 2 3 4. y = x \u0014 \u0015 1 2 14 0 , P = 3. D = 0 1 5 1 \u0015 \u0014 \u0014 1 14 0 1 , P = 4. D = 0 1 5 2 \u0014 2 3 2 5. y = x 1 3 005 \u0015 \u0014 2 14 0 , P = 5. D = 1 0 1 1 2 \u0015 \u0015 \u0014 1 14 0 , P = 6. D = 2 0 1 2 1 \u0015 \u0014 2 6. y = x + 1 3 \u0014 10.0 points Find the x-intercept of the Least Squares Regression line y = mx + b that best fits the data points (2, 2), (1, 2), (0, 3), (1, 1) . 007 True or False? 1 4 1. TRUE 2. x-intercept = 3 4 2. FALSE 3. x-intercept = 5 4 4. x-intercept = 1 2 5. x-intercept = 1 006 10.0 points When u1 = \u0015 1 , 2 \u0014 \u0015 2 , u2 = 1 are eigenvectors of a symmetric 2 2 matrix A corresponding to eigenvalues 1 = 14 , 2 = 1 , find matrices D and P in an orthogonal diagonalization of A. \u0015 \u0014 \u0015 \u0014 1 1 0 1 2 , P = 1. D = 0 14 5 2 1 \u0014 1 2. D = 0 \u0015 \u0014 1 0 , P = 2 14 2 1 \u0015 1 2 \u0015 2 1 \u0015 10.0 points If AT = A and if vectors u and v satisfy Au = 3u and Av = 4v, then u v = 0. 1. x-intercept = \u0014 2