Homework 1 Solutions
2. Write the zero vector of M34 (F )
0 0 0 0
0 0 0 0
0 0 0 0
13. Let V denote the set of ordered pairs of real numbers. If (a1 , a2 ) and
(b1 , b2 ) are elements of V and c R, d
MTH 235 - HW#2
Due Thursday, Sept. 14, in class (Lorman) or
at Hylan 820 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
1.3: #1 (all), 8(all), 9, 12, 15.
Problems to
MTH 235 - HW#9 Solutions
Due Tuesday, Nov. 14, in class (Lorman) or
at Hylan 915 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
4.1: #2, 3; 4.2: #13, 16, 19, 28; 4.5
MTH 235 - HW#7
Due Thursday, Oct. 26, in class (Lorman) or
at Hylan 915 by 3:00 p.m. (Gafni)
Problems to hand in:
Give detailed reasons for your answers. Please write legibly, both sign and print
your
MTH 235 - HW#8
Due Thursday, Nov. 2, in class (Lorman) or
at Hylan 915 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
3.1: #1 (all), 2, 3, 5
3.2: #1 (all), 2(b)(c)(e
MTH 235 - HW#12
Due Thursday, Dec. 7, in class (Lorman) or
at Hylan 915 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
5.2: Review the problems from HW11.
6.1: #1, 2
MTH 235 - HW#11
Due Thursday, Nov. 30, in class (Lorman) or
at Hylan 915 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
5.1: 1(a-f), 2(a-c), 3(b,c), 4(a,c,h), 5, 6,
Homework 5 Solutions
SECTION 2.1
16. Let T : P (R) P (R) be dened by T (f (x) = f (x). T is linear.
Let f P (R).
Then f (x) = an xn + + a1 x + a0 .
Let g(x) =
an
x
n+1 n+1
+ +
a1
2
+ a0 x.
Note that T
MTH 235 - HW#4
Due Thursday, Sept. 28, in class (Lorman) or
at Hylan 820 by 3:00 p.m. (Gafni)
T.A. Belmiro Galo da Silva
1. Consider the following subset of M22 (R):
S=
1
1
1
1
0
,
1
1
1
0
,
1
0
0
MTH 235 - HW#1
Due Thursday, Sept. 7, in class (Lorman) or
at Hylan 820 by 3:00 p.m. (Gafni)
TA. Belmiro Galo.
Solutions:
1. Let Pn be the set of real polynomials of degree exactly equal n, i.e., thos
MTH 235 - HW#3
Due Thursday, Sept. 21, in class (Lorman) or
at Hylan 820 by 3:00 p.m. (Gafni)
Problems to do but not hand in: Friedberg, Insel and Spence,
1.4: #1 (all), 3(d), 4(d), 6, 11,
1.5: #1 (al
Math 235: Linear Algebra
Midterm Exam 1
February 25, 2014
NAME (please print legibly): mill/firms?
Student ID Number:
CIRCLE YOUR INSTRUCTOR: Fatima Mahmood Geordie Richards
0 Read all instruction
MTH 235: Linear Algebra
Midterm 1
0 13
i) Lwbw
Indicate your instructor with a check in the box:
February
NAME (please print legibly):
Your University ID Number:
Giorgis Petridis
M ark Herm
MTH 235 - Homework 3 Solutions
Question 1. This is done by modifying the proof of Theorem 1.9 as done in Example 6.
The set cfw_v1 , v2 is linearly independent as the vectors are not multiple of each
MTH 235 - Homework 9 Sections 4.1 - 4.3
Please answer the questions in the order they are listed, STAPLE the pages together
and write clearly in the front of the assignment
COURSE ID NUMBER
Names of
MTH 235 - Homework 4 Section 2.1
Question 1.
Discussion: We know how T acts on (1, 2) and (1, 3), which incidentally form a basis for R2 , so we
express (1, 0) as a linear combination of the two vecto
Homework 3 Solutions
SECTION 1.5
10. Give an example of three linearly dependent vectors in R3 such that
none of the three is a multiple of the other.
1
0
1
0 , 1 , 1
1
0
1
15. Let S = cfw_u1 , u2
Subspaces
Linear Independence & Dependence
Let V be a vector space of dim n 2. Let W1 and W2 be subspaces
of V s.t W1 = W2 = V . Show that dim(W1 W2 ) dim(V ) 2.
Since W1 , W2 = V , we see that dim(W1
Vector Spaces
Vector space V over a eld F is a set on which the operations
addition and scalar multiplication, are dened so that for all
x, y V and for all a F there exists a unique element x + y V
an
Math 235: Linear Algebra
Midterm Exam 2
November 19, 2013
NAME (please print legibly):
Your University ID Number:
Please circle your professors name:
Friedmann
Tucker
The presence of calculators, cel
Math 173Q
Practice Second Midterm
1.
(a) Let c, a1 , . . . , an be real numbers. True or false and explain: if there
are any real numbers (t1 , . . . , tn ) such that
a1 t1 + + an tn = 0
then there is
Practice Questions
1. Let T : R2 R2 be linear and suppose T 2 = T0 , where T0 denotes the zero map.
(a) Show that R(T ) = R(T 2 ).
Solution: Since T 2 = T0 and R(T 2 ) R(T ) we know 1 rank(T 2 ) rank(