Spring 2010
(331) Solutions for EXAM 2
Dr. A. Agarwal
1. Let B be the following matrix
0 0 B= 0 a
1 0 0 b
0 1 0 c
0 0 1 d
(a) For what values of a (and no restrictions on b, c, d) will B be invertible? Explain. ANS: Observe that the first three rows of B
Solutions for Selected problems of Homework 4
A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10
1. Q24,P.151 Here is the product AB as a combination of rows of 1 2 3 0 + 0 1 1 1 + 2 AB = 3 2 3 0 + 1 1 1 1 + 1 2 2 3 0 + 0 1 1 1 + 1
B 4 9 8 1 6 4 = 6 4 5
Solutions for Selected problems of Homework 3
A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10
1. Q12, P.100 a To show that the span is entire R3 , we need to show that any vector b R3 cab be expressed c as a linear combination of the given vectors. In
Solutions for Selected problems of Homework 2
A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10
1. Q14,P.41 Since points P, Q and R are all in the plane, this means the vectors P Q and P R will lie in the plane. P Q = (0, 1, 0) (1, 0, 0) = (1, 1, 0) and
Solutions for Selected problems of Homework 1
A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10
1. Q22,P.14 Here is an algebraic way of nding w as a linear combination of u and v. Linear combination means, we have to nd scalars c1 , c2 such that w = c1