Linear Algebra
Math 2318
HW3
UH honor code: By signing my name on this test I promise that I will not commit any acts
of academic dishonesty during, before, or after the administration of this test. Academic
honesty violations include (but are not limited to) the following: sharing questions, sharing
answers, using unauthorized software, getting online help, having others take the exam for
me, using notes or books, or using unauthorized formula sheets during the exam. If I am
caught in such an act, I understand that it will result in the cancellation of my exam score. In
addition, the Math Department and my instructor have the right to take appropriate actions
in response to any violations of UH Academic Honesty Policy.
Name and ID:
5 points
1. Can every ector in R4 be written as a linear combinatin of the columns of the matrix
B? Do the columns of B span R3 ? Show work.
1
3 −2
2
0
1
1 −5
B=
1
2 −3
7
−2 −8
2 −1
5 points
0
0
4
2. Let v1 = 0 , v2 = −3 , v3 = −1 . Does {v1 , v2 , v3 } span R3 ? Show
−2
8
−5
work.
Homework 3
Math 2318
5 points
3. Describe all solutions of Ax = 0 in parametric vector form, if A is row equivalent to
matrix
1 5 2 −6 9
0
0 0 1 −7 4 −8
0 0 0
0 0
1
0 0 0
0 0
0
5 points
4. Suppose Ax = b has a solution. Explain why the solution is unique when Ax = 0 has
only the trivial solution.
0
