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
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 e
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
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 cf
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 syste
Lecture 4: Ax = b and solution sets
Danny W. Crytser
March 28, 2014
Todays lecture
We saw in the previous lecture that solving systems of linear
equations is equivalent to solving certain vector equat
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
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
Lectur
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 ha
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
Lecture 7: Linear transformations
Danny W. Crytser
April 4, 2014
Todays lecture
1
We will review the concepts of sets and functions
Dan Crytser
Lecture 7: Linear transformations
Todays lecture
1
We wi
Lecture 3: Vector equations
Danny W. Crytser
March 26, 2014
Todays lecture
We have seen that the solution sets to linear equations can often
be described as lines in the plane.
Dan Crytser
Lecture 3:
Ungraded Quiz + Questionnaire
Math 22: 12 Section
March 28, 2014
1. Solve the linear system
x+ y =1
x + 2y = 1
Solution:
Write the augmented matrix
1
1
1
2
1
1
.
Subtract the rst from the second row,