MAT224H1F: Linear Algebra II
Problem Set #9
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
MAT224H1F: Linear Algebra II
Problem Set #8
Solutions to Tutorial Problems
Tutorial Problems
1. Consider the linear transformation T : P3 (R) P3 (R) defined by
T (p(x) = x2 p 00 (x) + xp 0 (x).
(a) Fi
MAT224H1F: Linear Algebra II
Problem Set #2
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
MAT224H1F: Linear Algebra II
Midterm #2 Review
G ENERAL Q UESTIONS
The following are some very general questions you should be able to answer. If you
have difficulty answering a particular question, r
MAT224H1F: Linear Algebra II
Problem Set #10 Solutions
Practice Problems
1. Consider the subspace of R4 defined by the equation x1 + x2 + 2x3 + 3x4 = 0.
(a) Find a basis for this subspace.
Solution: T
MAT224H1F: Linear Algebra II
Problem Set #9
Solutions to Tutorial Problems
1. In each part, determine if the given linear transformation T is diagonalizable. If it is
diagonalizable, find a basis of t
Last Name:
Given Name(s):
Student Number:
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University of Toronto
Faculty of Arts & Science
MAT224H1F: Linear Algebra II
Midterm #1
MAT224H1F: Linear Algebra II
Problem Set #8
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
Last Name: g
Given Name(s):
Student Number:
9F5651CF013454A84~BB9E97A1CECS9CB7 E
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#1 1 of 13
4' University of Toronto
Faculty of Arts & Science
MAT224H1F: Linear Algebra II
Midterm #
MAT224H1F: Linear Algebra II
Problem Set #1
Solutions to Tutorial Problems
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on whic
MAT224H1F: Linear Algebra II
Problem Set #6
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
MAT224H1F: Linear Algebra II
Problem Set #5
Solutions to Tutorial Problems
1. Consider the bases = cfw_1, x, x2 of P2 (R) and = cfw_e1 , e2 , e3 , e4 of R4 . Also, consider the
linear transformation
MAT224H1F: Linear Algebra II
Problem Set #3
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
MAT224H1F: Linear Algebra II
Problem Set #7
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
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MAT224H1F: Linear Algebra II
Problem Set #10
Instructions: This problem set consists of only practice problems since there will be no
tutorials in the coming week.
Practice Problems
1. Consider the su
MAT224H1F: Linear Algebra II
Problem Set #5
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
MAT224H1F: Linear Algebra II
Problem Set #4
Instructions: This problem set consists of two parts. The first part, called Tutorial Problems, contains the problems on which your tutorial will be based.
University of Toronto
Faculty of Arts & Science
MAT224H1S: Linear Algebra II
Midterm Test
July 18, 2016
SOLUTIONS
1
1. Let V and W be vector spaces. [8 marks]
(a) Let v1 , v2 , . . . , vn V . Define w