Practice Problems
Vectors
1. Let A(7, 1, 1), B(4, 2, 1), C(3, 0, 5),
and D(6, 9, 5) be points in 3-space.
(a) Find the vector AB.
(b) Find a vector equation for the line L that passes through C
and is
Practice Problems
Linear Programming
1. Solve the linear program by graphing the feasibility region.
Minimize z = 7x 14y
subject to
3x + 4y 12
x y 0
0 x, 0 y
2. Solve the linear program by graphing th
Practice Problems
Linear Systems
1. Solve the system or show that it is inconsistent. If the system has
innitely many solutions, express them parametrically.
8
> x + 2y + 3z =
>
>
< 2x + 5y
=
(a)
> 3x
Practice Problems
The Leontief Open Model
1. An economy has two industries: energy and material.
To produce $1 of energy requires 90 of energy and 30 of material.
To produce $1 of material requires 20
Practice Problems
Matrix Operations
0 5 1
1. Given A = 3 2
1 , B =
4 6
2
9
1
, D = 1 2 ; nd the following if dened.
5
5
5 3
1
0
(b) B 3
(a) AD
Math 201-105-RE
,C =
1 2
0 8
8 3 3 0
(c) D2
(d) CC T
(e)