CS3251, Homework 5 Solution
1. Problem Set 4.4, p. 228, # 6 Let Q1 and Q2 be two orthogonal matrices. Then (Q1 Q2 )T Q1 Q2 = QT QT Q1 Q2 = 2 1 QT IQ2 = I and, therefore, Q1 Q2 is orthogonal. 2 2. Problem Set 4.4, p. 230, # 22 a = (1, 1, 2)T , b = (1, -1,
CS3251, Homework 1 Solution 1. Since v = (3, 1)T we have v = 10 and the unit vector is u1 = v/ v = ( 3 , 1 )T . 10 10
2 1 2 Similarly, w = (2, 1, 2)T so w = 3 and the unit vector is u2 = w/ w = ( 3 , 3 , 3 )T . We want to find U1 u1 and U2 u2 . This impli
CS3251, Homework 3 Solution
1. Problem # 10 The following are subspaces: (a), (d), (e) 2. Problem # 23 If we add b to a matrix A then the column space gets larger unless b C(A) (i.e., is already a linear combination of the columns of A). Example, of a lar
CS3251, Homework 4 Solution
1. Problem Set 4.1, p. 191, # 5 (a) If Ax = b and AT y = 0 then y b because b C(A) and y N (AT ) C(A). (b) If AT y = c and Ax = 0 then x c because c C(AT ) and x N (A) C(AT ). 2. Problem Set 4.2, p. 203, # 7 We have a1 = (-1, 2
CS3251, Homework 4
Due date: Thursday, November 14, 2013, in class
Theory (10pts each problem, total 60pts). The problems below are from the textbook.
1. Problem Set 4.1, p. 191, # 5 (p. 203, # 5, 4th ed.)
2. Problem Set 4.2, p. 203, # 7 (p. 214, # 7, 4th
CS3251, Homework 3
Due dates: Theory Tuesday 10/22, Programming Thursday 10/31
Theory (10pts each problem, total 60pts). The problems below are from the textbook.
1. Problem Set 3.1, p. 119, # 10 (p. 128, #10, 4th ed.)
2. Problem Set 3.1, p. 121, # 23 (p.
CS3251, Homework 5
Due date: Thursday, 12/5/2013, in class
Theory (6pts each problem, total 30pts). The problems below are from the textbook.
1. Problem Set 4.4, p. 228, # 6 (p. 240, # 6, 4th ed.)
2. Problem Set 4.4, p. 230, # 22 (p. 242, # 22, 4th ed.)
3
CS3251, Homework 1
Due date: Tuesday, September 24, 2013, in class
Theory (10pts each problem, total 60pts). The problems in the rst four items below
are from the textbook.
1. Problem Set 1.2, p. 17, # 4 (p. 19, # 5, in 4th ed.)
2. Problem Set 2.1, p. 32,