Math 304
Quiz #5B - Solutions
Sections 3.5,3.6
1. [6 pts] Calculate the transition (change of basis) matrix from the standard basis
[1, 0, 0]T , [0, 1, 0]T , [0, 0, 1]T to the basis cfw_[3, 3, 2]T , [1, 3, 3]T , [3, 3, 3]T .
Solution: From the relation
x
Math 304
Quiz #6B - Solution
Sections 4.3
1. [15 pts] Let A be the matrix representing L with respect to the standard basis in R3 ,
where
331
A= 3 2 2
113
Find the matrix B representing L with respect to the basis (1, 0, 1)T , (0, 1, 1)T , (1, 1, 1)T .
S
Math 304
Quiz #7B
Sections 5.1,5.2
1. [8 pts] Use vector projection to nd the distance of the point (3,2,1) to the plane
2x + 2y + z = 0.
Solution: The distance is given by the length of the scalar projection of x = (3, 2, 1)
onto the normal of the plane,
Math 304
Quiz #8B - Solution
Sections 5.3,5.4
1. [8 pts] Find the best quadratic least squares t to the data
x
y
0
0
1
-1
2
2
3
5
4
10
Solution: The matrix A is given by
A=
1
1
1
1
1
00
11
24
39
4 16
Therefore, least squares equations are AT Ax = AT b or
Math 335, Chapter 2
Name_
Glossary
1 11 determinant
CWID_
Page
8th
Edition
9th
Edition
84
87
Content
If A = (a) is a 1 x 1 matrix, thus det(A) = a
then A
will be nonsingular only if det(A) 0
2 22 determinant
3 Minor of aij for a matrix
4
Cofactor Aij of
Name:_
Glossary
1 Two-dimensional vectors
CWID_
Page
8th
Editio
n
Content
9th
Editio
n
111
113
2
Length (magnitude) of a
vector
103
106
3
Euclidean vector spaces
R2
110
112
A two dimensional vector is a grouping
of two scalars a and b and is denoted
a
b
b
Name_ _
Glossary
Page
8th Edition
9th
Edition
Linear equations and linear
systems
1
1
2 Solutions to linear systems
2
2
3 Consistent systems
2
2
4 Inconsistent systems
2
2
5 Equivalent systems
3~5
3~5
6 Triangular forms
5
5
7 Back substitutes
5
5
8 Elemen
Name_
ELVIS ONDEGO_
CWID_
Page
Glossary
8th
Ed
1 Linear transformation
2
Equivalent definition
linear transformation
Let
16
6
169
16
7
170
16
8
171
Content
Let V and W to be two vector spaces,L
is said to be a linear transformation
from V to W if
L( v 1+