MATH 210
Exam 1
February 10, 1997
1.
Which of the following represents the same line as 3x + 2y = 1?(a)
(b)
(c)
(d)
(e)
None of the above.
2.
The slope of the line passing through the points ( 4, 5 ) and ( 1, -1 ) is:(a)
1/2
(b)
2
(c)
4/3
(d)
-2
(e)
None of the above.
3.
Find the y-intercept of the line through ( 3, 5 ) and ( 1, 1 ).(a)
( 0, -1 )
(b)
( 0, 5 )
(c)
( 0, 1 )
(d)
( 0, 2 )
(e)
None of the above.
4.
Find the point of intersection of the straight lines 2x - y = 1 and 3x + 2y = 12.(a)
( 2, 3 )
(b)
( 10/7, 27/7 )
(c)
( 22/7, 51/7 )
(d)
( 4, 3 )
(e)
None of the above.
5.
How many corners has the feasible set for the following system of inequalities?
(a)
2
(b)
3
(c)
4
(d)
5
(e)
6
6.
Give an equation for the line parallel to the line 5x + 3y = 100 and passing through the point ( 1, 2 ).(a)
3x + 5y = 13
(b)
5x + 3y = 8
(c)
5x - 3y = -1
(d)
5x + 3y = 11
(e)
None of the above.
7.
Let
If possible, find the entry in the second row and the first column of the matrix product AB.
(a)
4
(b)
8
(c)
-3
(d)
13
(e)
None of the above.
8.
Find all solutions of the following system of equations:x + y + z = 1
2x + y + z = 2
x + y - z = 5
(a)
There is a unique solution. In the solution: x = 1.
(b)
There is a unique solution. In the solution: x = 2.
(c)
There is a unique solution. In the solution: x = 3.
(d)
There are infinitely many solutions.
(e)
There are no solutions; the system of equations is inconsistent.
9.
Find all solutions of the following system of equations:x + y + 2z = 1
2x + y + z = 2
3x + 2y + 3z = 3
(a)
There is a unique solution. In the solution: x = 1.
(b)
There are no solutions; the system of equations is inconsistent.
(c)
There are infinitely many solutions. In the set of all solutions, z = any value, x = 2 + z, y = -3z + 2
(d)
There are infinitely many solutions. In the set of all solutions, z = any value, x = 1 + z, y = -3z
(e)
None of the above.
10.
Find all solutions of the following system of equations:x + y + 2z = 1
2x + y + z = 2
3x + 2y + 3z = 4
(a)
There is a unique solution. In the solution: x = 1.
(b)
There are no solutions; the system of equations is inconsistent.
(c)
There are infinitely many solutions. In the set of all solutions, z = any value, x = 2 + z, y = -3z + 2
(d)
There are infinitely many solutions. In the set of all solutions, z = any value, x = 1 + z, y = -3z
(e)
None of the above.
11.
Let:
Given
solve the system
x - 3y - 2w = 117
3x - 12y - 2z - 6w = 2
-2x + 10y + 2z + 5w = 3
-x + 6y + z + 3w = -2
In the solution, x=
(a)
1
(b)
2
(c)
3
(d)
4
(e)
None of the above.
12.
If possible, find the inverse of
The entry in the third row and third column of
is:
(a)
1
(b)
6
(c)
1/4
(d)
5
(e)
The matrix is not invertible.
13.
Which of the following matrices are invertible?
(a)
All of them.
(b)
All except C.
(c)
A only.
(d)
A and D only.
(e)
A and B only.
For the next two problems consider the following:
A sector of an economy has 2 industries: oil and gas. The production of $1 of oil requires $0.90 in oil and $0.20 in gas, while the production of $1 of gas requires $0.40 of oil and $0.10 of gas. Assume there is an external demand for $300 of oil and $100 of gas.
14.
How much oil should be produced to satisfy demand?(a)
$1,500
(b)
$31,000
(c)
$4,000
(d)
$2,000
(e)
$1,880
15.
How much gas should be produced to satisfy demand?(a)
$1,500
(b)
$500
(c)
$4,000
(d)
$7,000
(e)
$1,880
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 8/2/97 by Dr. Anders Linnér (
alinner@math.niu.edu)