MATH 210
Exam 1
September 23, 1996
1.
Which equation describes the same line as 3x + 2y = 6?(a)
(b)
(c)
(d)
(e)
None of the above.
2.
The slope of the line passing through the points ( -1, -3 ) and ( -4, -7 ) is:(a)
4/3
(b)
3/4
(c)
11/5
(d)
-4/3
(e)
None of the above.
3.
Find t so that the three points ( t, 0 ), ( 2, 4 ) and ( 10, 8 ) lie on the same line.(a)
-4
(b)
-5
(c)
-6
(d)
-7
(e)
None of the above.
4.
How many corners has the feasible set for the following system of inequalities?
(a)
2
(b)
3
(c)
4
(d)
5
(e)
6
5.
Find the point of intersection of the straight lines 2x - y = 3 and 3x + 2y = -1.(a)
( 5/7, -11/7 )
(b)
( -1/7, -2/7 )
(c)
( -8, -13 )
(d)
( -1, 1 )
(e)
None of the above.
6.
Give an equation for the line parallel to the line 1499x + 6499y =4358 and passing through the point ( 1, 1 ).(a)
1499x + 6499y = 7998
(b)
6499x - 1499y = 5000
(c)
1499x - 6499y = -5000
(d)
6499x + 1499y = 7998
(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)
The product is undefined.
8.
Solve the system:2x + 4y = 30
2x + 2y + 6z = 30
6x + 4y + 4z = 50
(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:3x + 5y + 7z = 1
5x +4y - 8z = 7
8x + 9y - z = 2
(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 + 7z = 9
y - 2z = 5
II.
x - y + 4z - 3w = 12
z+2w = 8
w = 2
III.
x + 5y - 7z = 9
y - 2z = 1
3y - 6z = 11
IV.
x + 2y - z = 2
2y - z = 4
4y - 2z = 8
(a)
I and II only.
(b)
III and IV only.
(c)
I, II and III only.
(d)
I, II and IV only.
(e)
I, II, III and IV.
11.
Let:
Given
solve the system
x - 3y - 2w = 117
3x - 12y - 2z - 6w = 5
-2x + 10y + 2z + 5w = 97
-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)
1/6
(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 simple economy has 2 industries: food and power. The production of $1 of food requires 90 cents in food and 10 cents in power, while the production of $1 of power requires 20 cents of food and 60 cents of power. Assume there is an external demand for $100 of food and $200 of power.
14.
How much food should be produced to satisfy demand?(a)
$1,500
(b)
$500
(c)
$4,000
(d)
$2,000
(e)
$1,880
15.
How much power should be produced to satisfy demand?(a)
$1,500
(b)
$500
(c)
$4,000
(d)
$2,000
(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)