Linear Algebra - Midterm IIB Your Name: Do not open this until you are told to do so. Please turn off your cell phone. Show all your work on this booklet. The blue books are for scratch work only. Calculators, books, class notes and formula sheets ar
Math V2010: Linear Algebra
Section 003
Monday 05/04/2015
Instructor: Gabriele Di Cerbo
Practice Exam
Name:
170 minutes
Student ID:
Instructions.
(1) Use no books or notes or calculators or cell phones.
(2) For Question 1 and 2, indicate your answers clear
MATH 2010 Final Exam Review Session
Prof. Dave Bayer / Alex Dang
This is it, less than two weeks and youll be free from linear algebra! Youve all worked hard this semester, so make sure you
make this last exam count. As always, feel free to email me at ap
F15 Exam 1 Problem 1
[Reserved for Score]
Linear Algebra, Dave Bayer
testlalpl
Te s t l
Name,
U n i .
[1] Solve the following system of equations.
V"
0
H
-r
r
1
11 2
N
(
O
C
3
1
w
5
_1 2 3 5 8_
a>\
4
X
H
6
V
z
sum of (Dre\J\OUS +^0
w
V^v\C 'Z_
*Z
0
u
y
,0
Chapter 3
Chapter 3
Section 3.1
3.1.1 Find 3115 such that A5: 6:
|:1 0:|ﬁ|:1 0:|,sothatE1:E2:0.
3 4: 0 0 1: U
ker(A) =
3.1.3 Find all E such that AE : 6; note that all E in R2 satisfy the equation, so that ker(A) : R2 : span(€1,€2).
3.1.5 Find all a such
Section 3.2
3.1.43 Using our work in Exercise 42 as a guide, we come up with the following procedure to express the image of
an n X m matrix A as the kernel of a matrix B:
If rank(A) 2 11, let B be the n X n zero matrix.
If 1‘ 2 rank(A) < 11, let B be the
Section 3.3
j = 1: Yes, because is in ker(A) (the ﬁrst column is
COCOCOH
j : 2: No, this would just be a multiple of the second column, and only (1 if the jth component is zero.
0
2
71
j : 3: Yes, since 0 is in ker(A).
0
0
0
At this point, we realize tha
Section 2.4 Chapter 2
Section 2.4 2.4.21 : :52 fails to be invertible, since the equation : $2 : 1 has two solutions, m : :1.
2 3: 1 0 1 05 8 ,3 2 3 ‘1 8 _3 2.4.23 Note that f’(z) = 312 + 1 is always positive; this implies that the function f(m) = 13 +
Section 2.2
1 5/8 1/170 =1:
. . . . . . 8/5 1 >1 2 ,
to converting currency J to currency 1. This gives us 3 more entries: 170 * 1 * . Next, let 5
* 1/2 >1 1
ﬁnd the entry (141, giving the value of one Euro expressed in Pounds. Now E1 2 $(8/5) 2 $1.60 and
Section 2.2
1 5/8 1/170 =1:
. . . . . . 8/5 1 >1 2 ,
to converting currency J to currency 1. This gives us 3 more entries: 170 * 1 * . Next, let 5
* 1/2 >1 1
ﬁnd the entry (141, giving the value of one Euro expressed in Pounds. Now E1 2 $(8/5) 2 $1.60 and
Chapter 1 Section 1.3
coins, the second has 12, and the third is the richest, with 20 coins.
1.3.15 [1234] :5-1+6-2+7-3+4-8:70eitherway.
mama:
Section 1.3
13-1 a No solution, since the last raw indicates 0 = 1. 1.3.17 Undeﬁned, since the matrix has three
Math V2010: Linear Algebra
Section 003
Thursday 03/28/2016
Instructor: Gabriele Di Cerbo
Second Midterm Exam
Name:
75 minutes
Student ID:
Instructions.
(1) Use no books or notes or calculators or cell phones.
(2) Show all the steps of your work clearly. L
Math V2010: Linear Algebra
Section 003
Sunday 05/10/2015
Instructor: Gabriele Di Cerbo
Final Exam
Name:
170 minutes
Student ID:
Instructions.
(1) Use no books or notes or calculators or cell phones.
(2) Show all the steps of your work clearly. Little or n
Math V2010: Linear Algebra
Section 002
Thursday 02/17/2016
Instructor: Gabriele Di Cerbo
Practice Midterm
Name:
75 minutes
Student ID:
Instructions.
(1) Use no books or notes or calculators or cell phones.
(2) Show all the steps of your work clearly. Litt
Depends on Quiz 2, Students don't understand the reduced row echelon form, I
will give:
Type1: The Problem 5 in Quiz 2 (will be at least 20 points in Final)
-Understanding how to use a reduced row echolon form to tell linear
relations among vectors, and g
Linear Algebra Homework 5
YOUR NAME:
Instructions: You should print out the homework and write your answer on it. Write your UNI
in the right top corner of each page. and your name in the left top corner. For computational
exercises, circle the final answ
Homework 4
YOUR NAME:
Instructions: You should print out the homework and write your answer on it. Write your UNI
in the right top corner of each page. and your name in the left top corner. For computational
exercises, circle the final answer. This homewo
Linear Algebra Homework 7
YOUR NAME:
Instructions: You should print out the homework and write your answer on it. Write your UNI
in the right top corner of each page. and your name in the left top corner. For computational
exercises, circle the final answ
Solu of Homwk 9
YOUR NAME:
6:15 - 7:55 Monday,Aug,11th,2016, 100 minutes. No calculator.
Problem 1. Suppose
e1 e2
another orthonormal
basis
span v1 v2
w1
4 2
are orthonormal basis for V. v1 v2 = e1 e2
Find
3 1
w2 for the space. Such that span(w1 ) = span(
Extra Problems To Survive on Final
YOUR NAME:
1. What the coordinate do with the vectors
1.1. Understanding of coordinate matrix and reduced row echelon form.
Problem 1. Let V = Px2 = cfw_x2 a + xb + c, where a, b, c R be a right linear space.Let f, g, h
Homework 3
YOUR NAME:
Instructions: You should print out the homework and write your answer on it. Write your UNI
in the right top corner of each page. and your name in the left top corner. For computational
exercises, circle the final answer. This homewo
Homework 9
YOUR NAME:
Homework 9 does not need to submit. Solutions are attached.
4 2
Problem 1. Suppose e1 e2 are orthonormal basis for V. v1 v2 = e1 e2
Find
3 1
w
w
w
w
another orthonormal
basis
for
the
space.
Such
that
span(w
)
=
span(v
)
and
span
=
1
Linear Algebra Homework 6
YOUR NAME:
Instructions: You should print out the homework and write your answer on it. Write your UNI
in the right top corner of each page. and your name in the left top corner. For computational
exercises, circle the final answ
Final Review Problems
YOUR NAME:
1. Matrix Multiplication
1.1. Fully understand what happend in the product if AB=C. a
In the following, P is 3 3 matrix. P is not assumed to be invertible.
Problem 1. Suppose
1 1 1
1 2 5
1 4 7 P = a b c
1 2 3
1 0 2
What
Math V2010: Linear Algebra
Section 002
Thursday 02/17/2016
Instructor: Gabriele Di Cerbo
Practice Midterm
Name:
75 minutes
Student ID:
Instructions.
(1) Use no books or notes or calculators or cell phones.
(2) Show all the steps of your work clearly. Litt