Printed: February 27, 2013
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Linear Algebra MATH 2076 Quiz-7
This is a take-home quiz. Be sure to show your work. No credit for inspired answers!
Consider the following vector spaces and the three vectors there. For each case, prove eith
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Linear Algebra MATH 2076 Quiz-8 Answer: Key
Printed: November 8, 2013
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3
Find the characteristic polynomial of A = 0
2
Then nd all three eigenvalues of A. Hint: = 5
3
det(A I ) = det 0
2
11
5
Printed: October 14, 2013
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Linear Algebra MATH 2076 Quiz-7
This is a take-home quiz. Be sure to show your work. No credit for inspired answers!
Consider the following vector spaces and the three vectors there. For each case, prove either linear indene
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MATH 2076 Exam-2-2013s Answer: Key
Printed: October 1, 2013
Be sure to show your work. No credit for inspired answers! No calculators/computers/cell
phones.
1
1
1. Let A =
1
1
1
2
2
2
11
2 2
a 3
3a
(a) Compute det A. Hint: Gaussian elimination works
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Printed: September 28, 2013
MATH 2076 Exam-1 Answer: Key
Be sure to show your work. No credit for inspired answers! No calculators/computers/cell phones.
1. Explain/dene what does it mean for a system of linear equations to be consistent. Then nd all
AAE 539 Homework # 3
Spring 2016
1. Consider a solid rocket motor with a cylindrical center perforation (CP) grain. Assume
the propellant has a burning rate law:
r 0.025 Pc0.3 , Pc in psi, r in inches/sec
and that we require a liftoff thrust of 1.0 Mlbf.
AAE539
Homework#2
Problem 1
i)
Explain the quantitative nature of the plot.
The above exhaust species vary in these semi-logarithmic patterns due to changes in the exit
conditions of the supersonic flow. Most species have specific heats which vary with
te
AAE 539 Homework #5
Spring, 2016
Consider a solid rocket motor with a grain design as shown in the sketch below. We will load
the motor with a composite propellant with the following characteristics:
Composition: 15% Aluminum, 15% HTPB, 70% AP, p = 0.06 l
AAE539
HW4
Problem 1
problem 2
Engine
Propellants
Mixture
Pc,
At
2
Ratio
Psi/MPa
in /cm
2
Tc, Deg R
Deg K
hg,BTU/in2-F
2
Kw/cm -K
qdot,
BTU/in2-s,
Kw/cm2
RD-180
LOX/RP-1
2.72
3721.67
67.5
3883.88
0.000323
0.9257
Mer
AAE539
HW3
Due: 2/10/16
Problem 1
i) & ii) The results for parts (i) and (ii) can be found in the two following figures. The
methodology is included after the results and the entire source code for this pro
The heat transfer unit is W/m^2, not W/cm^2. Please check that!
Material Temperature Profiles
Material Temperature (K)
2500
2000
1500
Melting temp
1000
500
0
0
t = 1 sec
0.02
t = 2 sec
0.04
0.06
x (meters)
t = 5 sec
t = 10 sec
0.08
0.1
t = 15 sec
W W W W W W .u m . W ., ,
. W _ . W _ W W W W W W WW W
. . W n W _ m . 4 W . W W . W
L W W . W _ W W W W W W W W W W W
. W W W W W W . W W W W W W W W W W W
., W W W W F W W W n W. W W W W .
W W W W . W W W W _. W W W W W W W _
W. W W m M W W W W W W W W
I, ' E'- A rocket is operating at sea level with a chamber pressure of 65 Am The;
pmpellant combination produces a C of 1520 m/s and a 3 value of 1.2. The
nozzle throat area and expansion ratio are 0.1 m and 25 respectively. Calculate
the thrust and speci
Printed: October 7, 2013
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Linear Algebra MATH 2076 Quiz-5 Answer: Key
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1 1 0 0
1 1 1 1 1
0 0 1 1
2 2 2 2 3
Assume that A =
1 1 2 2 3 is row equivalent to B = 0 0 0 0
0000
1 1 1 1 2
(Do not ver
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Linear Algebra MATH 2076 Quiz-10 Answer: Key
Printed: November 22, 2013
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2
1
2
0
2
1
Suppose y = and v1 = , v2 =
2
2
1
0
1
2
Verify that vectors v1 , v2 are orthogonal
Find the distance fro
Printed: September 19, 2013
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Linear Algebra MATH 2076 Quiz-4
Complete the following definitions. Turn in on Monday.
Denition 1 (pg 30) The span of three vectors u, v, w in Rn , denoted by Spancfw_u, v, w, is .
Denition 2 (pg 65) A mapping T : Rn Rm is
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Printed: September 14, 2013
Linear Algebra MATH 2076 Quiz-3 Answer: Key
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3
6
9
1. Find the value(s) of h for which the vectors v1 = 6, v2 = 4 , and v3 = h are linearly dependent. Justify
1
3
3
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MATH 2076 Exam-2-2013s
Printed: October 18, 2013
Be sure to show your work. No credit for inspired answers! No calculators/computers/cell
phones.
1
1
1. Let A =
1
1
1
2
2
2
11
2 2
a 3
3a
(a) Compute det A. Hint: Gaussian elimination works well here.
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Printed: October 31, 2013
MATH 2076 Exam-2 Answer: Key
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a
1. If d
g
a
bc
e f = 2, nd 3d + 2a
5g
hi
b
c
3e + 2b 3f + 2c
5h
5i
Answer: We use properties of
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MATH 2076 Final-Exam-2012f Answer: Key
Printed: December 6, 2013
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phones.
0111
0 1 2 2
1. Reduce matrix A =
0 2 3 3 to echelon form. Circle the pivots. What is t
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Printed: September 6, 2013
Linear Algebra MATH 2076 Quiz-2 Answer: Key
Be sure to show your work. No credit for inspired answers!
2
1. Use Gaussian elmination to determine if vector b = 1 is a linear combination of the vectors formed from the
6
105
c
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MATH 2076 Final-Exam-2013s Answer: Key
Printed: April 28, 2013
Be sure to show your work. No credit for inspired answers! No calculators/computers/cell
phones.
0
0
1. Reduce matrix A =
0
1
Answer:
1
1
2
4
1
2
3
6
1
2
to echelon form. Circle the piv
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Printed: October 11, 2013
Linear Algebra MATH 2076 Quiz-6 Answer: Key
Be sure to show your work. No credit for inspired answers!
Be sure to show your work. No credit for inspired answers!
a
b
c
abc
If d e f = 17, nd 2d + a 2e + b 2f + c
3g
3h
3i
ghi