Unformatted text preview: Math 601 HOMEWORK 4 1. For each of the following matrices 12
1001
12
A=
, B = 0 0 , C =
48
0101
21
a) ﬁnd the null space.
b) Find the column space.
c) Is the matrix invertible? If so, ﬁnd its inverse, and check your answer.
d) Does the matrix have a left inverse? If so, ﬁnd it, and check your answer.
e) Does the matrix have a right inverse? If so, ﬁnd it, and check your answer.
2. Construct a matrix which transforms the standard basis vectors e1 , e2 , e3
of R3 into three given vectors v1 , v2 , v3 ∈ R3 . When is this matrix invertible?
3. Describe the linear transformation of the plane R2 which are represented in the standard basis by the matrices
A1 = 0 −1
10 −1 0
01 , A2 = , A3 = 01
00 4. Let A be an n × n (square) matrix.
a) Show that the null space of A2 contains the nulls pace of A.
b) Show that the column space of A2 is contained in the column space of A. 1 ...
View
Full
Document
This note was uploaded on 11/09/2011 for the course MATH 601 taught by Professor Un during the Winter '08 term at Ohio State.
 Winter '08
 un
 Linear Algebra, Algebra, Matrices

Click to edit the document details