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