Introduction to Linear Algebra for Science and Engineering, 3rd edition BY Daniel Norman
Email: richard@qwconsultancy.com
Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Let u = -4 , v = -7 . Find u + v . -1
1)
-9
A) -3
B) -13
-8
C)
-8
-5 -16
D) -11 -10
2) Let u = 2 , v = 2 . Find u - v. 4
A) -7
B)
-2
3) Let u = 8 , v = 8
A)
2)
9
0 -5
C)
4 13
D) -2 -7
4 . Find v - u. -1
3)
B) 12
0 -5
C)
7
-9 -4
D) -4 -9
4) Let u = -5 . Find 6u.
4)
-2
A)
30 -12
C) 30
B) -30 12
12
D) -30 -12
5) Let u = -3 . Find 7u.
5)
2
A) -21 14
B) -21
C)
-14
21 -14
D) -21 -14
6) Let u = -2 . Find -9u.
6)
-3
A)
18 -27
B) 18
C) -18
27
27
1
D) -18 -27
7) Let u = A)
5 , v = -2 . Find 2u + v. -6 -3 6 -15
B)
7)
6 -9
C) -2 -5
D)
8) Let u = -3 and v = -2 . Display the vectors u, v, and u + v on the same axes. 5
2
A)
B)
C)
D)
2
8 -15
8)
9) Let u =
5 . Display the vector 2u using the given axes. -4
A)
B)
C)
D)
10) Consider the points P(1,2,2), Q(-1, 0, 1), and R(3, 2, 1). Then A) PQ + RP = QR
B) PQ + PR = QR
C) PQ + PR = PR
D) QP + PR = QR
3
9)
10)
11) Find a vector equation of the line passing through the point P(1, -1, 3) and parallel to the line with 2 4 an equation X = 1 + t -2 , t 2 2
2
4
2
2
1
2
3
2
A) X = 1 + t -2 , t
C) X = -1 + t 1 , t
.
.
2
1
2
3
B) X = 1 + t -1 , t
.
1
2
3
1
.
D) X = -1 + t -1 , t
.
12) Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). -2
1
3
1
3
1
-2
1
A) X = 1 + t 1 , t
C) X = 0 + t 1 , t
11)
.
2
1
3
-5
-2
5
3
-5
B) X = 1 + t 1 , t
.
D) X = 1 + t -1 , t
12)
.
.
13) Find the parametric equations for the line passing through the points P(5,-1) and Q(2,3). A) x1 = -3 + 5t B) x1 = 2 - 3t C) x1 = 5 + 2t D) x1 = 3 + 2t
13)
14) Find the parametric equations of the line passing through the point (1,-1,2) and parallel to the line
14)
x2 = 4 - t
x 2 = 3 + 4t
x 2 = -1 + 3t
x 2 = -4 + 3t
x 1 = 2 + 5t, x 2 = 3 - 2t, x 3 = -2 + t.
A) x1 = 1 + 5t, x 2 = 4 - 2t, x 3 = -4 + t C) x1 = 1 + 2t, x 2 = -1 + 3t, x 3 = 2 - 2t
B) x1 = 1 + 5t, x 2 = -1 - 2t, x 3 = 2 + t D) x1 = 7 + 5t, x 2 = 5 - 2t, x 3 = t 1
0
0
1
15) Determine which vector from the options below is in the plane: x = s -1 + t 2 . 0
1
A) 3 0
1
2
C) 8
B) 1 1
D) 3 3
-1
16) Determine a scalar equation for the line through the points P(3,1), Q(0,-2). (x 1 - 3)
A) x2 = x1 - 2
B) x2 = 1 -
x -3 C) x2 = 3 + 1
x D) x2 = -2 + 1
3
3
3
4
15)
16)