Please note that these are some problems for practice and not a complete
review of the material for Midterm 2.
1.
1
1
3
0
A=
1
0
4 5
0
1
0
0
0
0
,
1
0
1
0
1
0
0 1
0
3
B=
8
0 100
2
3
9
2 34
a. Calculate AB using the definition.
b. Find a proper par
Matrix Algebra - MATH 110
First Midterm Test
October 4, 2013
Instructions: This question paper has seven pages plus cover. For each
question, write out your solution/answer carefully in the space provided.
Use the back of pages if necessary. Marks will be
Matrix Algebra - MATH 110
First Midterm Test
October, 2013
Instructions: This question paper has seven pages plus cover. For each
question, write out your solution/answer carefully in the space provided.
Use the back of pages if necessary. Marks will be d
Math 110 - Tutorial 2
Due at the beginning of tutorial on September 28
1. Consider the line y = 4x + 3 in R2 . Write the equation for this line in each of the following
forms:
(a) general
(b) normal
(c) vector
(d) parametric
Solution: Remember that for no
Matrix Algebra - MATH 110
Second Midterm Test
November 22, 2013
Instructions: This question paper has seven pages plus cover. For each
question, write out your solution/answer carefully in the space provided.
Use the back of pages if necessary. Marks will
Matrix Algebra - MATH 110
Second Midterm Test
November 22, 2013
Instructions: This question paper has seven pages plus cover. For each
question, write out your solution/answer carefully in the space provided.
Use the back of pages if necessary. Marks will
Math 110 - Tutorial 1
Due at the beginning of tutorial on September 21
1
1
1. Consider the vectors u = 0 and v = 1. Calculate each of the following:
2
3
(a) 2u 3v
(b) the unit vector in the direction of v
(c) the distance between u and v
(d) the project
Math 110 - Tutorial 3
Due at the beginning of tutorial October 5
0
1
1
0 1 0
1. Describe all vectors in the span of
,
,
2 1 0.
1
1
0
x
y
Solution: Were interested in knowing for which values of x, y, z, w we can write
z =
w
0
1
1
0
+ s 1
Math 110 - Tutorial 3
Due at the beginning of tutorial October 5
0
1
1
0 1 0
1. Describe all vectors in the span of
,
,
2 1 0.
1
1
0
k
3
1
5 , 2 ?
2. For which values of k is the vector 1 in the span of
2
2
6
3. Determine if each of the follow
Math 110 - Tutorial 2
Due at the beginning of tutorial on September 28
1. Consider the line y = 4x + 3 in R2 . Write the equation for this line in each of the following
forms:
(a) general
(b) normal
(c) vector
(d) parametric
2. Consider the point A = (2,
Math 110 - Tutorial 1
Due at the beginning of tutorial on September 21
1
1
1. Consider the vectors u = 0 and v = 1. Calculate each of the following:
2
3
(a) 2u 3v
(b) the unit vector in the direction of v
(c) the distance between u and v
(d) the project
MATH 110 - MATLAB PROJECT 1
DUE AT THE BEGINNING OF LECTURE ON TUESDAY, OCTOBER 25.
This project is intended to familiarize you with the basics of MATLAB, as well as to point out
some areas where using MATLAB requires care.
Instructions: After completing
MATH 110 - MATLAB PROJECT 2
DUE AT THE BEGINNING OF LECTURE ON TUESDAY, NOVEMBER 29.
In this project we will see how MATLAB handles eigenvalues and eigenvectors. We will continue
our investigation of cases where MATLAB must be used with care. We will also
Here are some Math110 problems for practice only. This is not a complete overview of final exam
material. The solutions will not be provided.
Part 1 (True/False):
1. A linearly independent set of vectors in Rn has at most n vectors.
2. If A is an n n matr
Please note that these are some problems for practice and not a complete
review of the material for Midterm 1.
1. Several questions can be answered by solving a system of linear equations. Here are
some examples. Consider the following system of linear eq
Mathematics 110
Fall 2012
University of Victoria
HW # 6, in preparation for Quiz 6.
Quiz will be in the beginning of the lecture on October 24, 2012.
Problem #1:
0
1 0
8 1
(a) Find the P T LU factorization of the matrix A = 8
2 2 0
2
2
(b) Solve Ax = B
Mathematics 110
University of Victoria
Fall 2012
HW # 7, in preparation for Quiz 7.
Quiz will be in the beginning of the lecture on October 31, 2012.
Problem #1: Find the coordinates of the vector v relative to the two bases B1 and B2 :
1
1
0
1
2
Mathematics 110
Fall 2012
University of Victoria
HW # 2, in preparation for Quiz 2.
Quiz will be in the beginning of the lecture on September 19, 2012.
Problem #1:
(a) Write definition of a unit vector.
(b) Define the projection of u onto v.
(c) True of F
Mathematics 110
University of Victoria
Fall 2012
HW # 1, in preparation for Quiz 1.
Quiz will be in the beginning of the lecture on September 12, 2012.
Problem #1:
(a) Write definition of a vector as a linear combination of other vectors.
(b) True or Fals
Mathematics 110
University of Victoria
Fall 2012
HW # 8, in preparation for Quiz 8.
Quiz will be in the beginning of the lecture on Friday November 16, 2012.
4
1
1
0 3 .
Problem #1: Consider the matrix A = 5
1 1
2
1
1. Find the eigenvalue of A correspondi
Mathematics 110
University of Victoria
Fall 2012
HW # 9, in preparation for Quiz 9.
Quiz will be in the beginning of the lecture on Wednesday November 28,
2012.
1 2
8
0 and compute (if
Problem #1: Find a matrix P that diagonalizes A = 0 1
0
0 1
1000
2011
Mathematics 110
University of Victoria
Fall 2012
HW # 5, in preparation for Quiz 5.
Quiz will be in the beginning of the lecture on October 17, 2012.
Problem #1:
Find the inverse of the coefficient
using the inverse:
x1
2x1
x1
matrix, and solve the linea
Mathematics 110
Fall 2012
University of Victoria
HW # 3, in preparation for Quiz 3.
Quiz will be in the beginning of the lecture on September 26, 2012.
Problem #1:
Consider the point B = (1, 0, 0), and the line ` given in the general form below
x+y+z =4
x
Mathematics 110
University of Victoria
Fall 2012
HW # 4, in preparation for Quiz 4.
Quiz will be in the beginning of the lecture on October 10, 2012.
Problem #1:
(a) Prove the following property of Matrix Multiplication: (A + B)C = AC + BC.
(b) Prove that
Mathematics 110 University of Victoria Fall 2010
HW # 3 ' Due 27 October 2010
1. Consider A and B as given
Uu {A}; {A};
,gw 5 0 0
A=1j%3£4, B=[030].
3m 0 0 4
i. Compute AB and BA.
ii. Explain how the columns or rows of A change when A is multiplied by
Please note that these are some problems
plete review of the course.
(1)
1 3 4 1
9
2 6 6 1 10
A=
3 9 6 6 3 , B =
3 9 4
9
0
for practice and not a com-
1
0
0
0
3
0
0
0
05
2 3
00
00
7
8
.
5
0
Suppose matrix B is an echelon form of the matrix A and nd th
Material covered after MIDTERM 2
Material from sections 4.4, 5.1 5.4, complex numbers
Eigenvalues, Eigenvectors (continuing)
Similar matrices
Determining of A is diagonalizable, Find A = PDP-1 or D = P-1AP
Diagonalization theorem (Th 4.27)
Orthogonality
O