Math 22, Exam II
May 13, 2010
NAME:
This is a closed book exam and you may not use a calculator. Use the
space provided to answer the questions and if you need more space, please
use the back of the exam making sure to write a note in the space provided
t
Math 22 Review for Midterm 2
Just as for the rst midterm, the exam will contain questions much like those from the
homework. If youve been doing well there and understand your answers and the concepts
behind them, youll do well.
Vector Space Terminology/C
Math 22, Exam I
April 22, 2010
NAME:
This is a closed book exam and you may not use a calculator. Use the
space provided to answer the questions and if you need more space, please
use the back of the exam making sure to write a note in the space provided
Lecture 8: The matrix of a linear transformation.
Applications
Danny W. Crytser
April 7, 2014
Example
Let T : R2 R3 be the linear transformation dened by
x1 + x2
x1
T
= 2x1 .
x2
3x2
Dan Crytser
Lecture 8: The matrix of a linear transformation. Application
Lecture 6: Linear independence
Danny W. Crytser
April 2, 2014
Todays lecture
1
Suppose we have vectors a1 , . . . , ap in Rn .
Dan Crytser
Lecture 6: Linear independence
Todays lecture
1
Suppose we have vectors a1 , . . . , ap in Rn . When does the
homoge
Math 22: Linear Algebra
Danny W. Crytser
Dartmouth College
March 24, 2014
What is a linear equation?
Dan Crytser
Math 22: Linear Algebra
What is a linear equation?
A linear equation is an equation of the form
a1 x1 + . . . + an xn = c
where the a1 , . . .
Ungraded Quiz + Questionnaire 3
Your name:
May 3, 2014
1. Let V = P2 and let B = cfw_1, t, t2 be the standard basis for P2 . Compute [1 4t + 7t2 ]B .
If 1 4t + 7t2 = c1 (1) + c2 (t) + c3 (t2 ) then
c1
1
c2 = 4 .
c3
7
This is the B-coordinate vector [1
Ungraded Quiz + Questionnaire 3
Your name:
April 25, 2014
1. Is cfw_1, t a basis for the vector space P2 of all polynomials with degree 2?
NO. Any basis for P2 has three elements, because the basis cfw_1, t, t2 has three elements. Thus cfw_1, t is
not a
Ungraded Quiz 2 + Questionnaire 2
Your name:
April 7, 2014
1. Is the system
2000293x + 9323909y + 2014z = 0
323123x
407y + 2187z = 0
consistent?
Yes. It is a homogeneous system, and homogeneous systems are always consistent (the zero vector is
a solution
Row reduction and echelon forms
Danny W. Crytser
March 25, 2014
Todays lecture
Dan Crytser
Row reduction and echelon forms
Todays lecture
Yesterday we sort of saw a way to solve systems of linear equations
by manipulating rows in the aliated augmented mat
Lecture 5: Homogeneous, inhomogeneous, solution
sets. Applications
Danny W. Crytser
March 31, 2014
Todays lecture
1
Finish up with homogeneous equations, learning when they
have a nontrivial solution.
2
Describe the solution set homogeneous equation as th