Multiple Choice Questions

Name:
Tutorial Seven 1
Math 1119 SectionE
Winter 2004
Part I
Multiple Choice Questions
Instructions: Circle the correct answer for each question. The value of each
question is 3 marks
1. Let A =
⎡
⎢
(a) ⎣
⎡
⎢
⎣
1 2 3
0 −1 4
4 6 1
−25 16 11
16 −11 −4
4 2 −1
⎤
⎥
⎦ . What is adjA?
⎤
⎥
⎦ ; (b)
⎡
⎢
⎣
−25 16 4
16 −11 2
11 −4 −1
a
2. Let A =
c
b
. What is adjA?
d
−a
(a)
c
b d
; (b)
−d −c
−b
a
; (c)
3. Let A =
(a)
⎡
⎢
⎣
⎡
⎢
⎣
1 2 3
0 −1 4
⎤
4 6 1
1
0
2
−1
⎤
3
⎥
4 ⎦; (b)
4 6 1
⎥
⎦ . b =
⎡
⎢
⎣
1
2
1
⎡
⎢
⎣
1
2
1
⎤
2 3
−1 4
6 1
d −c
−b a
⎤
⎥
⎦ ;(c)
⎡
⎢
⎣
; (d)
⎥
⎦ . What is A2(b)?
⎤
⎥
⎦ ; (c)
⎡
⎢
⎣
1 3
0 4
4 1
1
2
1
⎤
−25 −16 11
−16 −11 4
4 −2 −1
a −b
−c d
⎥
⎦ 0; (d)
⎡
⎢
⎣
.
1 1 3
0 2 4
4 1 1
⎤
⎥
⎦ ;(b)
⎡
1
⎢ 0
4. Let A = ⎢
⎣ 0
2
1
2
3
2
5
⎤ ⎡ ⎤
⎡ ⎤
4
1
x1
3 ⎥ ⎢
⎥ ⎢ 3 ⎥
⎢ ⎥
⎥
⎢ x2 ⎥
⎥ , b = ⎢ ⎥ . det A = 3. Let ⎢ ⎥ be the unique
7 ⎦ ⎣ 0 ⎦ ⎣ x3 ⎦
0 1 0 4
0
x4
solution of Ax = b. What is x2 determined by Cramer’s Rule?
(a) 10; (b) 20; (c) 30;(d) 40;
⎤
⎥
⎦ ;
⎡
⎢
⎣
−25 −16 4
−16 −11 −2
11 4 −1

Tutorial Seven 2
5. Let A be a 3 × 3 matrix det A = 5. What is det(2A)?
(a) 10, (b) 20; (c) 40; (d) 100;
6. Let det A = 4. What is det A −1 ?
(a) 4; (b) 2; (c) 1 1 ; (d) 4 2 .
7. Which of the following is a probability vector?
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤
.1 .3 .1 .1
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
(a) ⎣ .0 ⎦ ;(b) ⎣ .4 ⎦; (c) ⎣ .6 ⎦; (d) ⎣ .4 ⎦;.
.4 .1 .3 .4
8. Which of the following is a stochastic matrix?
⎡
.1
⎢
(a) ⎣ .0
.2
.1
⎤ ⎡
.3 .1
⎥ ⎢
.4 ⎦; (b) ⎣ .2
.2
.1
⎤ ⎡
.3 .1
⎥ ⎢
.4 ⎦ ; (c) ⎣ .0
.3
.4
.4 .6 .1 .1 .6 .1 .4 .1
.1
.2
.1
⎤
⎥
⎦ 0; (d)
⎡
⎢
⎣
.1 .7
.5 .4
.4 .1
9. Which of the following is a regular stochastic matrix?
⎡
.6
⎢
(a) ⎣ .0
.3
.1
⎤ ⎡
.3 .7
⎥ ⎢
.4 ⎦; (b) ⎣ .2
.4
.0
⎤ ⎡
.0 .3
⎥ ⎢
.6 ⎦ ; (c) ⎣ .3
.0
.4
⎤ ⎡
.5 .1
⎥ ⎢
.2 ⎦ 0; (d) ⎣ .5
.6
.3
.4 .6 .3 .1 .6 .4 .4 .6 .3 .4 .1
10. What is the steady-state vector for the stochastic matrix
(a)
.8
.2
;(b)
.4
.6
;(c)
.6
.4
;(d)
Part II
Long Answer Questions
.8 .3
.2 .7
Instructions: Solve the following questions. The value of each question is 10 marks
1. Let A =
⎡
⎢
⎣
1 −3 2
−3 8 −5
2 −6 5
(a) Find adjA and A −1 ;
⎤
⎥
⎦ . b =
⎡
⎢
⎣
2
5
4
⎤
.3
.7
⎥
⎦ .
(b) Using Cramer’s rule, solve the linear system Ax = b;
?
.3
.2
.5
.3
.2
.5
⎤
⎥
⎦ ;
⎤
⎥
⎦ ;