Homework 3 NAME:
Due Date: Weds Sept 21, 2016
Be sure to include a justification for how you arrived at your answers.
1. (a) Find the general solution of the homogeneous system. Write your solution in vector form.
x1 +2x2 3x3 =
5
2x1 +x2 3x3 = 13
x1 +x2
=
Homework 4 NAME:
Due Date: Weds Sept 28, 2016
Be sure to include a justification for how you arrived at your answers.
1. If v 1 , v 2 are linearly independent and v 3 Spancfw_v 1 , v 2 , show that v 1 , v 2 , v 3 are linearly dependent.
2. Let A be a nonz
1. Answer True or False. Justify your answer.
Homework 10 NAME: % [e Due Date: Wednesday November 16, 2016
@( Be sure to include a @cation for how you arrived at your answers.
)det (AT) =( 1) ).det(A)
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True @
(b) If A = PDP1 for some matrices
Homework 4 NAME: Keg: Due Date: Weds Sept 28, 2016
Be sure to include a ju ication for how you arrived at your answers.
1. If v1, :2 are linearly independent and v3 6 Spancfw_v1, '02, show that '01, 112,123 are linearly dependent.
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Homework 5 NAME: g Due Date: Monday Oct 3, 2016
Be sure to 1nclude a Justl catlon for how you arrlved at your answers
122
oot
(b) For your answer in (b) show t
Homework 6 NAME: \< Due Date: Weds Oct 12
Be sure to include a justic ' for how you arrived at your answers.
1. Answer T/F. Justify your answer.
(a) B2 is a subspace of R3. FAL$E
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(b) The columns of an invertible n
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Homework 10 NAME:
Due Date: Wednesday November 16, 2016
Be sure to include a justification for how you arrived at your answers.
1. Answer True or False. Justify your answer.
(a) det(AT ) = (1) det(A).
(b) If A = P DP
1
for some matrices P, P
1
True
False
Homework 9 NAME:
Due Date: Wednesday November 09, 2016
Be sure to include a justification for how you arrived at your answers.
1. In the following A is an m n matrix. Answer True or False. Justify your answer.
(a) dim(Row(AT ) = dim(Col(AT ).
True
False
(
Math 2184  Linear Algebra I
Fall 2016 (Aug 29  Dec 12)
MW 02:2003:35 in Bell 108
CRN: 12550
I NSTRUCTOR :
C ONTACT:
O FFICE H OURS :
T EXTBOOK :
Frank Baginski, Phillips 714, 2115 G Street NW
[email protected] or 2029946269
MW 05:1006:40 PM or by app
Homework 1 NAME:
Due Date: Wed/Sept 7, 2016
Be sure to include a justification for how you arrived at your answers.
1. Consider the system of linear equations:
x1 6x2
x2 4x3 +x4
x1 +6x2 +x3 +5x4
x2 +5x3 +4x4
=
=
=
=
5
0
3
0
Is the system consistent or not
Homework 5 NAME:
Due Date: Monday Oct 3, 2016
Be sure to include a justification for how you arrived at your answers.
1 2 2
1 1 .
1. Let A = 2
1
0 0
(a) Find A1 .
3
(b) If b = 0 , use A1 to find the solution of Ax = b.
2
2. Let A =
3 4
,
7 8
(a) Find A1 .
Homework 8 NAME:
Due Date: Wednesday November 02, 2016
Be sure to include a justification for how you arrived at your answers.
1. If Q is a 5 5 matrix such that Col(Q) = IR5 , what can you say about solutions of Qx = b for b 2 IR5 .
2. If the columns of A