MATH 247
Group #:
Group.Quiz.1
Members:
8.26.13
Rating:
1. (4 points) List four possible expected student learning outcomes.
2. (4 points) Brainstorm and describe a winning strategy for you to get an A in this class.
3. (2 points) List two biggest challen
MATH 247
Group #:
Group.Quiz.14
Members:
10.21.13
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3
2
4 2 1
3
2
2 5 7 3, u = , v = 1.
1. (5 points) Let A =
1
3
7 8 6
3
0
(a) Is u N(A)? Why or why not? Could u be in Col(A)? Why or why not?
(b) Is v Col(A)? Why or why not? Could v be in N(A)? W
MATH 247
Group #:
Group.Quiz.13
10.14.13
Members:
Rating:
1. (2 points each) Let V denote a vector space and H a subset of V . Determine if H is a subspace
of V in the following items. Be sure to justify your answer.
(a) V = R2 . H = the union of the rst
MATH 247
Group #:
Group.Quiz.15
Members:
1
1
1. (5 points) Let A =
2
3
10.23.13
Rating:
2 3 4 8
2 0
2 8
.
4 3 10 9
6 0
6 9
(a) (3 points) Find a basis for N(A). Justify your answer. In complete sentences, give a recipe
for nding a basis for the null spac
MATH 247
Group #:
Group.Quiz.7
9.18.13
Members:
Rating:
1. (1 point) In your own words (whatever makes the most sense for you), state a working denition
of linear independence.
2. (2 points) Let
1
v1 = 2 ,
3
4
v2 = 5 ,
6
2
v3 = 1 .
0
Determine if cf
MATH 247
Group #:
Group.Quiz.11
10.7.13
Members:
Rating:
1. (3 points) Prove the following.
(a) If A is invertible, then A1 is also invertible and A1
1
= A.
(b) If A and B are n n invertible matrices, then so is AB, and (AB)1 = B 1 A1 .
1
T
(c) If A is in
MATH 247
Group #:
Group.Quiz.9
Members:
9.30.13
Rating:
We now want to look at the solutions of the matrix equation Ax = b by examining the properties of
the transformation A. Particularly, I want you to look for the connection between the one-to-oneness
MATH 247
Group #:
Group.Quiz.10
10.2.13
Members:
Rating:
1. (2 points) Use very little energy to multiply
1
1 0 0 0
0 2 3 4 5
0 0 3 0 1
3
0 0 0 4
2
6
0
1
3
7
2
6
4
8
4
0
and justify your reasoning.
2. (1 point) Suppose the third column of B is the sum of
MATH 247
Group.Quiz.8
Group #:
Members:
9.25.13
Rating:
1. (4 points) Let
1 3
3
3
2
4 , u =
A= 3
, b = 2 , c = 2 ,
1
1 7
5
5
and dene a transformation T : R2 R3 by T (x) = Ax so that
1 3
x1 3x2
x
4 1 = 3x1 + 4x2 .
T (x) = Ax = 3
x2
1 7
x1 + 7x2
(a) Fi
MATH 247
Group #:
Group.Quiz.6
Members:
9.16.13
Rating:
1. (2 points) Let A be an m n matrix and b Rm . What can you say about the system Ax = b
if
(a) A has a pivot position in every row.
(b) the columns of A span Rm .
Summarize what you noticed from doi
MATH 247
Group #:
Group.Quiz.2
Members:
8.28.13
Rating:
1. (4 points) Suppose CheapNFast have ights that originate from seven cities: Los Angeles, San
Francisco, Seattle, Chicago, Denver, Las Vegas, and New York with destination cities indicated
by the fo
MATH 247
Group #:
Group.Quiz.5
9.11.13
Members:
Rating:
1. (1 point) Give an example of an augmented matrix of size 4 7 that is in the row echelon form
but not in the reduced row echelon form. Justify your answer.
2. (4 points) Given a linear system of eq
MATH 247
Group.Quiz.4
Group #:
Members:
1. (4 points) Let u =
9.9.13
Rating:
1
2
and v =
. Answer the following questions.
1
1
5
1
(a) (1 point) display the vectors w = u v and z = 3u + 3v on the graph paper.
2
2
www.PrintablePaper.net
(b) (1 point) What
MATH 247
Group #:
Group.Quiz.3
9.4.13
Members:
Rating:
1. (3 points) Solve the following system of equations in matrix notations. What does your solution
set mean geometrically?
x1 + x2 + x3 =
2
2x1 + 3x2 + x3 =
3
x1 x2 2x3 = 6
2. (3 points) Given an augm
MATH 247
Group #:
Group.Quiz.12
Members:
10.9.13
Rating:
1. (3 points) Determine whether
0
3 5
0
2
A= 1
4 9 7
is invertible. Provide 6 distinct reasons to justify your answer.
2. (3 points) Let U be a square matrix such that U T U = I. A matrix that satis