Math 2210
Final exam
Monday 12 December 2011
Solutions
1 (20 points).
(a) Row reduce:
1
2
0
2
1
12
1
0 0 0
A = 1 2 1
1
2 3 7 2
00
21
3 1 = rref( A).
00
1
0
A basis of Col( A) is formed by the pivot columns of A, namely 1 and 1 . So
1
3
dim(Col( A) = 2.
(b
Sept. 27, 2011
Math 2210 Prelim 1 Solutions
Time: 90 mins.
1) (20 points) Let
A
"
"
"
#
"
(
"
"
&
#
"
"
,"
t
t
t
"
, b" " , b# " , b ,# .
"
#
,$
"
Find all solutions to the systems of equations a) At !, b) At b" , c) At b2 , where
x
xt
xt
%
t
t is in
Math 2210
Final exam
Tuesday 14 December 2010
2:004:30 pm
No books or electronic devices allowed. You are allowed a two-sided letter size paper of
notes.
Please show all work and justify your answers.
Put your name and student ID on the front cover of you
Math 2210 - Linear Algebra
Final exam - 6 December 2012 - 2:00pm to 4:30pm
Name and NetID:
What time do you attend lecture? Circle one. 9:05-9:55 10:10-11 11:15-12:05 12:20-1:10
Whose discussion section are you enrolled in? Circle one.
David Belanger
INST
Math 2210 - Linear Algebra
Second prelim - 5 November 2013 - 7:30 to 9:00pm
Name and NetID:
Whose discussion section are you enrolled in? Circle one. Yash Lodha Wai-kit Yeung
At what time is the discussion section you enrolled in? Circle one.
1:25-2:15pm
Math 2210 - Linear Algebra
Second prelim - 25 October 2012 - 7:30 to 9:00pm
Name and NetID:
What time do you attend lecture? Circle one. 9:05-9:55 10:10-11 11:15-12:05 12:20-1:10
INSTRUCTIONS
OFFICIAL USE ONLY
This test has 6 problems on 6 pages, worth a
Solution to Prelim 2
12 5
1. (20 points). Consider the matrix A = 3 4 11 .
5 6 17
(a). Find a basis for the column space of A.
(b). Find a basis for the row space of A.
(c). Find a basis for the null space of A.
(d). Without actually nding the space direc
October 27, 2011
Math 2210
Prelim 2
No books or electronic devices allowed. You are allowed a one-sided letter size paper of
notes.
Please show all work and justify your answers.
Put your name and student ID on the front cover of your exam booklet and sig
October 27, 2011
Math 2210
1 (20 points). Consider the matrix A =
Prelim 2 Solutions
122 4
.
3 6 8 16
(a) Find a basis for the column space of A.
(b) Find a basis for the null space of A.
(c) Find a basis for the row space of A.
(d) What is the rank of A?
Math 2210 - Linear Algebra
First prelim - 25 September 2012 - 7:30 to 9:00pm
Name and NetID:
Whose discussion section are you enrolled in? Circle one.
David Belanger
INSTRUCTIONS
Teddy Einstein
OFFICIAL USE ONLY
This test has 7 problems on 7 pages, worth
1. (20 points) Consider the system of linear equations
x + 3y + 2 z + w = a
2x + 8y + 5z + 2w = b
x + 5y + 3 z + w = c
(a) What are the constraints on the values of a, b, c in order for the system to be
consistent?
(b) Find all the solutions for the hom
Math 2210 - Linear Algebra
First prelim - 1 October 2013 - 7:30 to 9:00pm
Name and NetID:
Whose discussion section are you enrolled in? Circle one. Yash Lodha Wai-kit Yeung
At what time is the discussion section you enrolled in? Circle one.
1:25-2:15pm 2:
1.8 SOLUTIONS
20. Use the basic denition of As to construct A. Write
Ttx}-xv+rv[v v]x]3 Fl); A 3 Fl
It-22I2Jr25_2.5_2
31}. Given any x in R. there are constants cl. cp such that x = cm + (Fr... because v]. vp span
R. Then. from property (5) of a lin
Math 2210 - Linear Algebra
Final exam - 13 December 2013 - 9 to 11:30am
Name and NetID:
Whose discussion section are you enrolled in? Circle one.
Yash Lodha
Wai-kit Yeung
At what time is the discussion section you enrolled in? Circle one.
1:25-2:15pm
2:30