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Printed: October 11, 2013
Linear Algebra MATH 2076 Quiz-6 Answer: Key
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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
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Printed: September 28, 2013
MATH 2076 Exam-1 Answer: Key
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1. Explain/dene what does it mean for a system of linear equations to be consistent. Then nd all
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
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
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
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
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MATH 2076 Final-Exam-2013s Answer: Key
Printed: April 28, 2013
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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: September 6, 2013
Linear Algebra MATH 2076 Quiz-2 Answer: Key
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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-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
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
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
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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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
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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: 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 Answer: Key
Printed: October 1, 2013
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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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MATH 2076 Exam-2-2013s
Printed: October 18, 2013
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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
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