false

Study Guides
(247,996)

Canada
(121,214)

Western University
(12,847)

Mathematics
(105)

Mathematics 1229A/B
(28)

Vicki Olds
(10)

Midterm

Unlock Document

Mathematics

Mathematics 1229A/B

Vicki Olds

Fall

Description

Thursday, November 6, 2008 CODE 111 Mathematics 1229A
Page 1 Test 2
STUDENT NUMBER:
1. Consider the following systems of equations in the variables x,y and z.
x y z x y z √
(i) x + 5y − z = 3 (ii) − + = 3 (iii) − + = 3
2 3 4 2 3 4
2 3 4 1 x(y + 2z) = 1 2 1
x − y + z = 3 x + 5 y − z =
x + 5y − z = 3 3
x − y + z = √ 3 x − (y + 2z) = 1
2 3 4
Which of the above systems are linear in x,y and z?
A: all of them B: (i) only C: (ii) only D: (iii) only E: none of them
2. Find the augmented matrix for the following system of linear equations.
x − y − 2 = −z
z = 2x
▯1 −1 −2 −1 ▯ ▯ 1 −1 −1 −2 ▯ ▯ 1 −1 1 2 ▯
A: 0 0 1 2 B: 2 0 1 0 C: 2 0 1 0
▯ ▯ ▯ ▯
D: 1 −1 −2 −1 E: 1 −1 1 2
−2 0 1 0 −2 0 1 0
3. Which one of the following matrices is in row-reduced echelon form?
1 1 0 1 0 0 1 0 1 1 0 0 1 0 0
A: 0 1 0 B: 0 0 1 C: 0 1 1 D: 0 1 1 E: 0 0 0
0 0 1 0 0 1 0 0 0 0 0 1 0 0 1
−1 3 −1
4. Let A = 1 −4 2 and let B be the row-reduced echelon form of A. Then the
2 −6 2
ﬁrst row of B is
▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯
A: 1 0 −2 B: 1 0 2 C: 1 0 1 D: 1 0 0 E: 1 1 0
▯ ▯
1 1 y
5. Find all (x,y) so that the ma0 x 1 is in row-reduced echelon form.
A: (0,1) only B: (1,0) onlyC: (1,1) and (0,0)D: (1,1) only E: (0,0) only Mathematics 1229A CODE 111 Thursday, November 6, 2008
Test 2 Page 2
6. The system of linear equations
x1 − 2x 2 − 3x 3 + 2x 4 = 1
−x 1 + x2 + 3x 3 − 2x 4 = −2
−2x 1 + 4x 2 + 6x 3 − 4x 4 = −2
has
A: no solutions
B: exactly one solution
C: a one-parameter family of solutions
D: a two-parameter family of solutions
E: a three-parameter family of solutions
7. Find the augmented matrix in row-reduced echelon form for the given system
x − 2y − 3z = 1
−x + 2y + 3z = −1
x − 2y + 3z = −5
▯ ▯ ▯ ▯ ▯ ▯
1 −2 −3 1 1 −2 0 −2 1 0 0 2
A: −1 2 3 −1 B: 0 0 1 −1 C: 0 1 0 1
1 −2 3 −5 0 0 0 0 0 0 1 −1
▯ ▯ ▯ ▯
1 −2 −3 1 1 −2 −3 1
D: 0 0 0 0 E: 0 0 1 −1
0 0 −6 6 0 0 0 0
1 0 1 2
8. Let A = 0 1 −2 1 be the augmented matrix for a system of linear equations. The
0 0 0 0
solution to the system is
A: (2,1,0)B: (0,0,0) C: (2 − t,1 + 2t,D: (2 − t,1 + 2t,E: there is no solution
1 0 2 8
9. Let A = 0 3 0 6 be the augmented matrix for a system of linear equations.
0 0 −1 −4
The solution to the system is
A: (0,2,4) B: (8,2,4) C: (1,3,−1) D: (8,6,−4) E: there is no solution
10. Find the value(s) of k for which the system of linear equations with augmented matrix
1 0 0 3
0 1 3 2 has no solution.
0 2 k 4
A: k = 6 only B: k ▯= 6 C: k = −6 only D: k ▯= −6 E: no value of k Thursday, November 6, 2008 CODE 111 Mathematics 1229A
Page 3 Test 2
11. ind the vale(s) of k for which the system of linear equations with augmented matrix
1 0 0 3
0 1 2 2
has exactly one solution.
0 k 4 4
A: k = −2 only B: k ▯= 2 C: k = 2 only D: k ▯= −2 E: no value of k
1 0 0 1
12. The matrix 0 1 0 1 is the augmented matrix for a linear system of three
0 0 k − 4 k + 2
equations in three unknowns x,y and z. Which of the following are true?
(i) The system has no solution for k = 2.
(ii) The system has exactly one solution for k ▯= ±2.
(iii) The system has inﬁnitely many solutions for k = −2.
A: (i) only B: (ii) only C: (iii) only D: all of them E: none of them
13. Describe the region (point, line, or plane), if any, that is the intersection of these planes.
−x + 2y − z = 1
2x − 4y + 2z = −2
x − 2y + z = −1
A: a point B: a plane C: a line D: none of A,B or C E: all of A,B and C
▯ ▯
3 −2 7 8 4
14. If A = and B = 0 −1 then which of the following is not deﬁned?
0 8 1
−4 3
A: (BA) B: (A − B )T C: (A + B) D: (3A − 2B) E: (AB)T
15. For the matrices A and B from the previous question, what is AB

More
Less
Related notes for Mathematics 1229A/B

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.