Math 317: Linear Algebra
Homework 2
Due: September 11th, 2015
The following problems are for additional practice and are not to be turned in: (All
problems come from Linear Algebra: A Geometric Approach, 2nd Edition by ShifrinAdams.)
Exercises: Section 1.4: 1–8,11,13–15
Section 1.5: 1–4,7–12,14,15
Turn in the following problems.
1. Section 1.4, Problem 4(d)
2. Section 1.4, Problem 11(b)
3. Section 1.4, Problem 14
4. Suppose that [A|b] is the augmented matrix associated with a linear system. You
know that performing row operations on [A|b] does not change the solution of the
system. However, no mention of column operations was ever made because column
operations can alter the solution.
(a) Describe the effect on the solution of a linear system when the j th column of
A is interchanged with the k th column of A.
(b) Describe the effect when column A∗j (i.e. the j th column of A) is replaced by
cA∗j for some c ∈ R.
(c) By experimenting with a 2 × 2 system, describe the effect when A∗j is replaced
by A∗j + cA∗k where A∗k denotes the k th column of A.
5. Section 1.5, Problem 4(b)
6. Section 1.5, Problem 7(a)
7. Section 1.5, Problem 13
8. Section 1.5, Problem 15
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