HW 15
11 1
Let L : P4 M22 be the linear function given by
2a b
a
3
2
L(ax + bx + cx + d) =
.
d
c + 3d
(a) Show that L is invertible with inverse L1 : M22 P4 given by
= x3 + ( + 2)x2 + (3 )x + .
L1
HW 2
21
Let
5
A=
3
1 2
,
0 4
2 1
B = 8 6 ,
0 3
7 4
C = 2 0 ,
9 3
D= 1 9
3 .
Compute each of the following (or, if the expression is undefined, say so):
(a) B + C
(b) 4A
(c) AB
(d) BA
(e) BD
(f) DC
Sol
HW 16
12 3
Find the inverse of the matrix
by using the formula A1 =
Solution:
1 1
A = 1 2
1 4
1
3
9
1
Adj A (see Section 12.2).
det A
First,
1
det A = 1
1
1
2
4
= 1(+1)
1
3
9
2
4
1
3
1(1)
+
1
9
HW 3
31
Show directly from the definition that the function L : R3 R2 given by
2x1 x2 + 4x3
L(x) =
x1 6x3
is linear.
Solution:
First, the input vector x is an element of R3 (according to the notation
HW 1
11
In each case, sketch the lines to decide whether the system has a unique solution, no
solution, or infinitely many solutions. Then solve the system either by using the methods
of Section 1.1 o
HW 17
13 3
Let C be the vector space of all functions on R having derivatives of all orders. Let
L : C C be the linear function described by multiply by x and then take derivative.
For instance, L(sin
HW 14
10 5
Use a least squares solution to find a curve of the form y = a cos x + b sin x that best fits
the data points (0, 1), (/2, 2), and (, 0).
Solution: Ideally, the curve would go through all t
HW 11
8 10
Let CR denote the set of continuous functions on R (this is a vector space using function
addition and scalar multiplication). Define L : CR FR by
Z x
L(f )(x) =
f (t) dt.
0
Show that L is
HW 9
78
Find a basis for each of the spaces Null A, Row A, and
1
2
5
2
1 2 5 2
A=
0
1
3 2
2
3
7
6
Col A, where
4
3
.
8
0
Solution:
(Null A) Solving Ax = 0, we get
Homework List
1
2
5
2
4
1 2 5 2 3
0
HW 13
91
Find the angle between x = [1, 2, 1, 2]T and y = [2, 1, 1, 3]T using the inner product of
Section 9.3.
Solution:
We have
cos =
xT y
kxkkyk
2
1
1 2 1 2
1
3
p
= p
2
2
2
2
2
1 + 2 + (1) + 2 2
HW 12
8 17
Show that cfw_x2 1, 2x2 + x is a basis for the subspace S = Spancfw_x 2, x2 + x + 1 of P3 .
Solution:
We check the two properties of basis:
(i) (Spancfw_x2 1, 2x2 + x = S?) First,
x2 1 = 1(
HW 7
61
Show that cfw_b1 , b2 is a basis for R2 , where
2
4
b1 =
, b2 =
.
2
2
Solution:
We check the two properties:
(i) (Spancfw_b1 , b2 = R2 ?) Every linear combination of vectors in R2 is a v
HW 10
83
Show that FI satisfies property (V2).
Solution: Let f, g, h FI . We need to show that (f + g) + h =f + (g + h). Each side
represents a function, so we need to show that (f + g) + h (x) = f +
HW 6
48
Let S = Spancfw_[2, 4, 1]T .
(a) Give a geometrical description of S.
(b) Find two planes having S as their intersection. (Hint: Use the method for determining
S given in the solution to Examp
HW 4
38
Let L : R3 R2 be the linear function given by
2x1 x2 + 5x3
L(x) =
.
7x2 + 4x3
(a) Find the matrix of L.
(b) Use part (a) to find L([3, 2, 1]T ).
(c) Find L([3, 2, 1]T ) directly from the formu
Math 2250 Lab 3
Reanna Wang
The purpose of this lab is to design a robot to throw a ball into a cup across a table.
The robot will have a rotating arm of length r cm. The robot will be mounted on the
Math 2250 Lab 2
Reanna Wang
The purpose of this lab is to design a robot to throw a ball into a cup across a table. The
robot will have a rotating arm of length r cm. The robot will be mounted on
Math 2250 Lab 1
Reanna Wang
The lab we were given in class presents the problem a client has of tennis balls being
constantly thrown at their heads. In this scenario, we are hired to intercept these b
Math 2250 Test 3
Name:
For each problem, show your work and write clearly.
4
f ( x )= + ln ( x 2 ) on [1, 4].
x
1. Find the absolute max and absolute min values of
2. Identify critical points, local e
Next: About this document .
INTEGRATION OF TRIGONOMETRIC INTEGRALS
Recall the definitions of the trigonometric functions.
The following indefinite integrals involve all of these well-known trigonometr
skip to main content
My Home
MATH2250 Calculus I for Sci and Eng Fall 2017 30103
Select a course.
Loading.
Message alerts - You have new alerts
Instant Messages
Loading.
Update alerts - You have new a
NAME: W PreCakuss Review
Directions: Remember that this is a no-caicuiator assignment. You may leave your answers unsimplic. You may
work on this on your own or with a group, but you need to submit yo
8/31/2017
HW2 - MATH2250 Calculus I for Sci and Eng Fall 2017 30103
https:/uga.view.usg.edu/d2l/le/content/1370370/viewContent/21192258/View?ou=1370370
2/3
8/25/2017
HW1 - MATH2250 Calculus I for Sci and Eng Fall 2017 30103
https:/uga.view.usg.edu/d2l/le/content/1370370/viewContent/21141314/View?ou=1370370
2/3
8/25/2017
HW1 - MATH2250 Calculus I for Sci
MATH 2250: Calculus for Science and Engineering
Course Syllabus
Instructor. Nick Castro
www.math.uga.edu/ncastro
Office. Boyd Graduate Studies Research Center 434E.
Office Hours. TBA
Lecture. MWF 10:1
MATH 3510(H): Multivariable Mathematics (part II)
Spring 2017 Syllabus
Instructor: Professor Michael Usher (usher@uga.edu)
Scheduled Class Meetings: MWF 11:15-12:05 and T 11:00-12:15 in
Boyd 302.
Offi