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 parallel to AB.
(c) Is the point D on the line L?
Math
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 the feasibility region.
Maximize z = x + y
subject to
x +
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 + 6y + 9z =
>
>
:
4x + 9y + 11z =
1
0
3
8
8
> 3x + y +
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 of energy and 30 of material.
(a) Given an external de
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) A 2I
(f) B 1
6
1
3 1 2
3 2
2 3 1
; nd the following if