Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam II
March 30, 2015
Sections 1 and 2
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the exa
Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam 1
Feb 25, 2013
All sections
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the exam. Unle
Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam I
October 12, 2015
Sections 1 and 2
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the ex
Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam 2
Nov 5, 2012
All sections
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the exam. Unles
Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam 1
Feb 25, 2013
All sections
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned o and put away during the exam. Unless
1.3 VECTOR EQUATIONS
Key concepts to master: linear combinations of vectors and a
spanning set.
Vector: A matrix with only one column.
Vectors in R n (vectors with n entries):
u1
u
u2
un
Geometric Description of R 2
Vector
x1
x2
is the point x 1 , x 2 in
1.8
Introduction to Linear Transformations
Another way to view Ax b:
Matrix A is an object acting on x by multiplication to produce
a new vector Ax or b.
EXAMPLE:
2
4
3
6
1
2
8
2
3
2
4
3
6
1
2
12
4
2
1
0
0
0
Suppose A is m n. Solving Ax b amounts to findi
Math 70
Linear Algebra
TUFTS UNIVERSITY
Department of Mathematics
Exam II
November 16, 2015
Sections 1 and 2
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the