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Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
1 6 0 4
If A = 2 3 1 0 , determine (a) a32, and (b) the order of A.
4 7 2 8
2) Solve the matrix equation: x
5
y - 1 = 2y
2x
5
4
2x
1)
2)
3) Find the transpose of 5 0 4 .
953
3)
4) If A = 1 2 3 ; B = 2 -1 -2 , then find (A + B)T.
3 4 5
1 -3 -2
4)
5 2
7 -1
-8 3
5) If A = 2 1 , B = -2 9 , and C = 5 -2 , find 4A - 2B + 3C.
4 -3
1 -7
3 -3
5)
6)
6)
1
3
0
4
Solve the matrix equation: x 2 + 2 5 + y 3 = 3
3
1
0
x - y - 3
5 -2
7 5 0
2 -4
7) If A = -4 3 , B = -2 1 1 , and C = 5 7 , find BA - C.
1 4
1 -3 -5
-4 9
7)
7 5 0
8) If B = -2 1 1 and C = 6 8 , find BC.
2 -1
1 -3 -5
8)
9)
9)
4x
+ 6z = 3
Use matrix multiplication to represent the system: x - y + z = 4
3x + y - z = 5
1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
10) 1 -1 2
1 0
4
-1 2 3 + 0 1 =
0
-1 -1
10)
5
-7
B) 9 12
2 -3
C) 4 8
1 0
D) 2 9 -3
E) none of the above
A)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
11) Solve the following system of equations by reducing the matrix:
2x + y = 11
9x + 5y = 7
11)
12) Solve the following system of equations by reducing the matrix:
x - y - 3z = 2
2x - y - 4z = 3
x+y- z=1
12)
13) (a) If A is the coefficient matrix of the system x + 3y = 2 , determine A-1 .
x + 2y = 5
(b) Use A-1 to solve the system.
13)
14) Find y′ if y = 4x 3 - 6x 2 + 7x - 8.
14)
15)
15)
5
.
Find y′ if y = 4
4 x
16) Find y′ if y = x 4 + 4
.
x2
16)
17) Find y′ if y = x(x + 2).
17)
18) Let f(x) = 4x 2 - 3x + 1.
(a) Find f′(x).
(b) Evaluate f′(1).
(c) Find an equation of the tangent line to the graph of y = f(x) at the point (1, 2).
18)
19) Find all values of x for which the curve y = x 2 + 6x - 4 has a horizontal tangent line.
19)
2
20) Find all points x for which the curve y = 2x 2 + 3x + 5 has a tangent line that is perpendicular to
the line y = x + 15.
20)
21) Find yʹ if y = (x 3 - 10x + 2)(x 2 + 7x + 1).
21)
x 2 + 1.
.
2x 3 - 1
22)
22) Find yʹ if y = dy
23) If y = 4u2 - 13u + 3 and u = 7x 3 + 5x 2 + 4x -14, then by direct use of the chain rule find and
dx
23)
evaluate when x = 1.
24) Find yʹ if y = 5(2x 2 - 3x + 4)8 .
24)
25)
25)
4
Find yʹ if y = (2x + 5)3 .
26) Find yʹ if y = x 2 (2x - 5)5 .
26)
27) Find yʹ if y = ln(2x 2 - 3).
27)
28) Find yʹ if y = log2 (4x + 5).
28)
29) Find yʹ if y = log 5x + 3.
29)
30) Find yʹ if y = ln(x 2 ) + ln3 x.
30)
31) Find yʹ if y = ln (x 2 + 5)5 (3 - 4x)4 .
31)
32) Find yʹ if y = -3e4x 2 - 5x + 3.
32)
33) Find yʹ if y = 4 2x + 1.
33)
34) Find yʹ if y = 10x 2 + 1.
34)
3