Math 26 Castroconde
Quiz 6A (4.2, 4.3)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
2.
3.
4.
5.
3a + b
, a, b R is a subspace of R 3 and find a base for it
Math 26 Castroconde
Quiz 5A (4.1)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
a
Let W = , a, b R . Use the definition of subspace to show that W is a
2b
Math 26 Castroconde
Quiz 1A (1.1-1.3)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
Use matrices to solve the system below.
2 x1 + 2 x 2 3 x3 = 1
x1 + 3 x 2 +
Math 26 Worksheet 9
Name:
Note that some questions may not be graded.
Answer the following questions after reading section 2.9.
1. Suppose the set B = cfw_v1 , v2 , . . . , vn is a basis of the subsp
Math 26 Worksheet 16
Name:
Note that some questions may not be graded.
Answer the following questions after reading section 5.1.
1. Let A be an n n matrix. What is an eigenvector of a matrix A?
2. Wha
Math 26 Quiz 6
Name:
Answer the following questions. No partial credit.
1. Find the eigenvalues and corresponding eigenspaces of the following matrices. Determine which of the following
matrices are d
Math 26 Worksheet 4
Name:
Note that some questions may not be graded.
Answer the following questions after reading section 1.7.
1. Define what it means for the set cfw_v1 , v2 , . . . , vp Rn to be l
Math 26 Exam 1 Spring 2010
1. Let S = cfw_v1 , v2 , . . . , vp Rn . Define the following.
(a) span S
(b) S is linearly dependent (give both criteria)
2. Let T be a function from Rn to Rm . Define or
Math 26 Exam 2 Spring 2010
1 0 2
2 0 3
1. Consider the matrix A =
3 0 4
4 0 5
5 0 1
NOT have to verify this. Answer the
1
7
0
12
17
. After some arithmetic, we have rref(A) = 0
0
22
0
17
foll
Math 26 Chapter 4 Review
1. Define the following.
(a) subspace
(g) dimension
(b) null space of an m n matrix
(h) linear transformation of vector spaces
(c) column space of an m n matrix
(i) kernel
(d)
Math 26 Chapter 5 Review
1. Let A and B be n n matrices. Define the following.
(a) v is an eigenvector of A corresponding to the eigenvalue
(b) the eigenspace of A corresponding to the eigenvalue
(c
Math 26 Exam 3 Spring 2010
1. Consider the linear transformation T : R2 R2 satisfying
1
2
T (e1 ) =
, T (e2 ) =
.
2
1
1
1
,
. Notice that the given information uses vectors written with respect
Math 26 Castroconde
Quiz 1A (1.1, 1.2)
Name:
I.D.#:
1. The matrix below is the reduced row echelon form of the augmented matrix of a linear
system with variables 1 , 2 , ,
1 2 0 0 0 2
[0 0 1 0 1 3]
0
Math 26 Castroconde
Exam 1A (1.1-1.9)
Name:
I.D.#:
Use both sides of each page, if needed.
Number the solution of each problem carefully.
TO EARN FULL CREDIT YOU MUST SHOW ALL WORK.
No calculators or
Math 26 Castroconde
Quiz 4A (2.2-3.2)
Name:
I.D.#:
Start your work after the last question. Use the back of the page and attach more
paper, if needed.
1 1 2
1. Let A 1 2 3 . Use row operations on the
Math 26 Worksheet 15
Name:
Note that some questions may not be graded.
Answer the following questions after reading section 3.3.
1. Let A be an n n matrix and b Rn . What is the matrix Ai (b)?
2. What
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Kevin Lamarque/Reu
Math 26 Castroconde
Quiz 3A (1.6-1.8)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
2.
3.
1
0
2
2 , w = 2 , u = 2 are linearly dependent or
Determine if th
Math 26 Castroconde
Quiz 3B (1.6-1.8)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
2.
3.
1
0
1
2 , w = 2 , u = 2 are linearly dependent or
Determine if the
Math 26 Castroconde
Quiz 4A (3.1, 3.2)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
2.
3.
Compute the determinant of the matrix below in two ways: first using
Math 26 Castroconde
Quiz 4B (3.1, 3.2)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
2.
3.
Compute the determinant of the matrix below in two ways: first using
Math 26 Castroconde
Quiz 5B (4.1)
Name:
.D.#:
Do your work on a separate sheet of paper. Attach this page to your work before
turning it in for grading.
1.
3a
Let W = , a, b R . Use the definition o
W W
WWW H
maumceafﬂﬁ. Wm;mumMLUWIHW :ntary row
natrix A is
ltiplyiiig A
ble matrix
(c) If the columns of a ma-
trix are linearly iildepen—
dent, then its rows must
also be linearly indepen—
de
1. Consider the following system of equations where h E R is a real number.
$1+2$2—£B3=1
3:31—182-1—13312
5331+31L‘2—3133h
(a) For what va.lue(s) of h is the system of equations consistent?
, "2 ”i
m
Math 3A
Final exam review
2
1
1. Let u = 1 , v = 3 .
0
4
1. Compute u v, kvk, kuk,
vector in the direction of u;
anda unit
2/ 5
Answer: 1; 26; 5,
1/ 5 .
0
2. Find the
orthonormal
projection of v o
Project 1 - Matrices and Linear Systems of Equations
In this project you will learn how to enter matrices in Maple and how to
use them when solving linear systems of equations.
Basic Maple Key Strokes
Math 26 Castroconde
Quiz 2A (1.4, 1.5)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
2.
3.
4.
5.
G G
G
G
G G
Prove that if A is an m x n matrix and v , w R n , th
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Email address: [email protected]
Text (required): Assembly Language Programming Made
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Math 26 Castroconde
Quiz 3A (1.6-1.8)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
2.
3.
independent.
G G
Give an example of a 3 x 2 matrix A such that Ax = 0 ha