MATH 210
Exam 1
February 17, 1996
1.
The slope of the line passing through the points ( 1, -5 ) and ( -2, -3 ) is:(a)
8/3
(b)
-8
(c)
-2/3
(d)
-3/2
(e)
None of the above.
2.
Which of the following lines passes through the point ( 2, -1 )?(a)
5x + 2y = 3
(b)
5x - 2y = -7
(c)
-5x + 2y = -8
(d)
5x + 2y = 8
(e)
None of the above.
3.
Given:
Solve the system:
In the solution:
(a)
z = 0
(b)
z = 1
(c)
z = 2
(d)
z = 3
(e)
None of the above.
4.
Let A be the matrix of the above problem and let
What is the bottom left entry of
?
(a)
1
(b)
-1
(c)
-2
(d)
-3
(e)
None of the above.
5.
Given
The entry in the first row and first column of CD is:
(a)
-4
(b)
1
(c)
-7
(d)
CD is undefined.
(e)
None of the above.
6.
Find x so that the points ( 1, 3), ( 5, 7) and ( x, 1) lie on the same line.(a)
x = 3
(b)
x = -2
(c)
x = -5
(d)
x = 1
(e)
None of the above.
7.
Give an equation for the line parallel to the line 49x + 749y = 646 and passing through the point ( 1, 1).(a)
49x + 749y = 798
(b)
49x - 749y = 700
(c)
749x + 49y = 798
(d)
749x - 49y = 700
(e)
None of the above.
8.
Solve the system:x - 2y - 5z = 3
-2x + 3y + 5z = -2
3x - 2y - 5z = 3
(a)
In the solution: z = -1.
(b)
In the solution: z = -2.
(c)
In the solution: z = -3.
(d)
There are infinitely many solutions.
(e)
No solution; the system of equations is inconsistent.
9.
Solve the system:x - y + z = 1
2x - 3y - 7z = 5
2x - 4y - 6z = 9
(a)
In the solution: z = -1.
(b)
In the solution: z = -2.
(c)
In the solution: z = -3.
(d)
There are infinitely many solutions.
(e)
No solution; the equations are inconsistent.
10.
Which of the following systems have infinitely many solutions?I.
x - 2y + 5z = 7
y - 2z = 4
II.
x + y + 4z - 3w = 2
z+2w = 8
w = 3
III.
x + y - z = 1
y - 2z = 1
3y - 6z = 4
IV.
x + y - z = 2
y - z = 2
-4y + 4z = -8
(a)
I and II only.
(b)
III and IV only.
(c)
I, II and III only.
(d)
I, II and IV only.
(e)
Some other selection.
11.
Consider the system:x - y = 5
2x - 2y = k
Which of the following statements is true?
(a)
If k = 10 , the system has no solutions.
(b)
If k = 10 , the system has infinitely many solutions.
(c)
If k = 10 , the system has exactly one solution.
(d)
If k > 10 or k < 10, the system has exactly one solution.
(e)
None of the above.
12.
If possible, find the inverse of
The entry in the third row and second column of
is:
(a)
-3
(b)
1/6
(c)
1/3
(d)
The matrix A is not invertible.
(e)
None of the above.
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)
Some other selection.
For the next two problems consider the following:
Let a simple economy have 2 industries: food and labor. The production of $1 of food requires 90 cents in food and 10 cents in labor, while the production of $1 in labor requires 20 cents in food and 60 cents in labor. Assume there is an external demand for $10 in food and $20 in labor.
14.
How much food should be produced to satisfy demand?(a)
$180
(b)
$50
(c)
$400
(d)
$250
(e)
$150
15.
How much labor should be produced to satisfy demand?(a)
$180
(b)
$50
(c)
$400
(d)
$250
(e)
$150
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 9/18/97 by Dr. Anders Linnér (
alinner@math.niu.edu)