Math 2030, Matrix Theory and Linear Algebra I, Fall 2011
Answers to Homework 1
Copyright c 2011 J. Barger and P. Selinger. Do not redistribute.
Part I: True or false questions
Decide whether each statement is true or false. If it is false, give a reason.
Math 2030, Matrix Theory and Linear Algebra I, Fall 2015
Answers to the second midterm
c
Copyright 2015
P. Selinger. Do not redistribute.
Part I: True or false questions (2 points each)
Decide whether each statement is true or false. If it is false, give
Math 2030 - Linear Algebra, Fall 2016
Midterm 2
Full Name:
Student ID:
Instructions: To receive full credit, show all of your work and explain all your steps. Use the
back of each page if more space is needed. Put a box around the nal answer for each ques
ENGI 2102: Thermo-Fluid Engineering I
Fall 2016
Assignment 3 SOLUTIONS
TOTAL MARKS:
Problem 1
/ 20
[5 marks]
a) Let subscript 2 represent the 2.7 lb weight and subscript 1 represent the 1.2 lb weight.
Note that m = 2.7 lbm and mg = 2.7 lbf. For the potent
ENGI 2102: Thermo-Fluid Engineering I
Fall 2016
Assignment 2
Due: Friday, September 30th, 2016 by 1:30 pm
Bring your assignment to Thursdays lecture or office F105B on Friday before 1:30 pm
Problem 1
[5 marks]
Suppose that the temperature and pressure at
Question
Problem 1
Mark
Possible
Marks
1
16
2
6
3
5
4
8
Total
35
[16 marks]
Questions 1-3 are multiple choice questions. Clearly circle the correct answer.
1. Which of the following statements is true about incompressible fluids? [0.5 mark]
a)
b)
c)
d)
Th
ENGI 2102: Thermo-Fluid Engineering I
Fall 2016
Assignment 2 SOLUTIONS
TOTAL MARKS:
/ 20
Problem [5 marks]
a) From Example 2.3, the variation of pressure with altitude is given by,
g
z R
P P0 1
T0
Rearranging for z,
P
P
0
R
g
1
z
T0
R
T0 P g
z
1
P0
ENGI 2102: Thermo-Fluid Engineering I
Fall 2016
Assignment 1
Due: Friday, September 23rd, 2016 by 1:30 pm
Bring your assignment to Thursdays lecture or office F105B on Friday before 1:30 pm
Problem 1
[4 marks]
At standard temperature and pressure, propane
Question
Problem 1
Mark
Possible
Marks
1
16
2
6
3
5
4
8
Total
35
[17 marks]
Questions 1-3 are multiple choice questions. Clearly circle the correct answer.
1. Which of the following statements is true about incompressible fluids? [0.5 mark]
a)
b)
c)
d)
Th
Problem 1 Multiple Choice/Matching/Short Answer
[11 marks total]
Circle the correct answer.
1. A fluid is a form of matter that is:
[1 mark]
a) able to withstand an applied shear stress
b) unable to withstand any applied shear stress
2. For what type of m
ENGI 2102: Thermo-Fluid Engineering I
Fall 2016
Assignment 3
Due: Friday, October 7th, 2016 by 5 pm
Bring your assignment to Thursdays lecture or office F105B on Friday before 5 pm
Problem 1
[5 marks]
A 2.7 lbf weight is dropped 3 ft onto the lever and fu
Problem 1 Multiple Choice/Short Calculation
[11 marks total]
Circle the correct answer.
1. For an open, steady-flow system, which of the following is always true? [1 mark]
a) total mass flowrate in = total mass flowrate out
b) total volumetric flowrate in
Dalhousie University/Fall 2016 - MATH 2030
Assignment 1 Part B Solutions
Part B
1. Point-parallel form of the given lines are
L1 := cfw_(1, 0, 1) + s(2, 0, 1) : s R
and
L2 = cfw_(3, 1, 0) + t(1, 1, 1) : t R.
The shortest distance d is the length of the ve
Dalhousie University/Fall 2016 - MATH 2030
Assignment 3
Part A: Practice problems. Solve the following problems on your own and check your
answers against the posted solutions which will be available Friday, November 25.
1. Determine whether or not the ve
Dalhousie University/Fall 2016 - MATH 2030
Assignment 3 Part A solutions
Part A: Practice problems. Solve the following problems on your own and check your
answers against the posted solutions which will be available Friday, November 25.
1. Determine whet
Dalhousie University/Fall 2016 - MATH 2030
Assignment 1
Part A: Practice problems. Solve the following problems on your own and check your
answers against the posted solutions which will be available Sept. 30.
1. Find the shortest distance between the poi
M ATH 2030 H OMEWORK #3
D UE : W EDNESDAY F EBRUARY 1 IN CLASS
1. (Similar to Problem 1.18 and 1.22 in text) Let H be a hyperplane in R4 defined by the
equation x1 + x2 + x4 = 3
(a) Find the equation of a line passing through the point (1, 0, 1, 1) in R4
M ATH 2030 H OMEWORK #2
D UE : F RIDAY JANUARY 27 IN CLASS
1.
(a) (Similar to Problem 1.9 in text) Is there a scalar k so that the vectors u = (k 21 , 2)
and v = (1, 2k) in R2 are orthogonal?
1
.
Solution: We need to have u.v = k 21 + 4k = 0, which means
Dalhousie University/Fall 2016 - MATH 2030
Assignment 2
Part A: Practice problems. Solve the following problems on your own and check your
answers against the posted solutions which will be available Friday, Oct 29.
1. Let
and
1 3 2
A=
1 2 2
0
3
B = 1 1 .
M ATH 2030 H OMEWORK #5
D UE : F RIDAY F EBRUARY 17 IN CLASS
P LEASE S HOW A LL YOUR W ORK FOR F ULL C REDIT !
1. (Similar to Problem 2.8 in text) In each case below either find the product of the two matrices
or state that the product is not defined.
1 2
M ATH 2030 H OMEWORK #4
D UE : F RIDAY F EBRUARY 10 IN CLASS
P LEASE S HOW A LL YOUR W ORK FOR F ULL C REDIT !
1. (Similar to Problem 1.30 1.34 in text) If u = 1 + i and v = 2 i are complex numbers,
then
(a) Find |u|
(b) Simplify uv
u
v
(c) Simplify
Solut
Math 2030, Matrix Theory and Linear Algebra I, Fall 2015
Answers to the first midterm
c
Copyright 2015
P. Selinger. Do not redistribute.
Part I: True or false questions (2 points each)
Answer: True. We know that a b is orthogonal to the plane, so it is al
Math 2030, Matrix Theory and Linear Algebra I, Winter 2014
Answers to the second midterm
c
Copyright 2014
P. Selinger. Do not redistribute.
Answer: False. Indeed, the opposite is true: the vectors v1 , . . . , vn are
linearly dependent if and only if the
Math 2030, Matrix Theory and Linear Algebra I, Winter 2014
Answers to the first midterm
c
Copyright 2014
P. Selinger. Do not redistribute.
Part I: True or false questions
Answer: True. Its echelon form has at most 4 leading variables, so at
least 2 non-le
M ATH 2030 H OMEWORK #1
D UE : F RIDAY JANUARY 20 IN CLASS
1. (Similar to Problem 1.4 in text) Find x and y so that the two vectors in R2 are equal.
(x + y, 2) = (2x y, y)
0
3
4
2. (Similar to Problem 1.6 in text) Write the vector
6 in R as a linear com
Dalhousie University/Fall 2016
MATH 2030
1. For the following matrices check if they are invertible. For the invertible one, express it as
a product of elementary matrices.
2 7 1
(a) A = 1 4 1
1 3 0
1 4 2
(b) B = 1 2 0
1 3 1
1 0 2
(c) B = 1 2 0
1 0 1
Dalhousie University/Fall 2016 - MATH 2030
Assignment 2 Part A solutions
Part A: Practice problems. Solve the following problems on your own and check your
answers against the posted solutions which will be available Friday, Oct 29.
1. Let
1 3 2
A=
1 2 2
Dalhousie University/Fall 2016 - MATH 2030
Assignment 3 solutions
Part B : Solve the following problems and hand in your solutions to be marked. Write up
your solutions in the order the problems are given and put a box around the final answer for
each que