sparks (cns658) HW02 gilbert (57245)
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001
10.0 points
Equivalent linear systems can have dierent
solution sets.
1
1.
momin (akm2466) HW04 gilbert (56780)
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1
Explanation:
If w is in Spancfw_u, v, then w can be written as a linear comb
momin (akm2466) HW01 gilbert (56780)
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1
we see that
P =
4 2, 4 2 ,
while
001 10.0 points
The robotic arm shown in
4
sparks (cns658) HW01 gilbert (57245)
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001
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Which one of the points
P (2, 3, 6), Q(1, 2, 1), R(7, 4, 5)
in
Version 035 EXAM03 gilbert (57245)
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001
By denition, is a singular value of A
when = and is an eigenvalue of AT A;
1
Version 022 EXAM01 gilbert (56780)
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001
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If an n n matrix A has n pivot positions,
then the reduced echel
momin (akm2466) HW15 gilbert (56780)
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001
Thus x1 = x2 = x3 = 0, so B is a linearly
independent set of vectors in R3
Version 010 EXAM01 gilbert (57245)
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4 2
3 1
10
10
1. rref(A) =
1 2
0 0
2. rref(A) =
3
0
3. rref(A) =
Version 099 FINAL gilbert (57245)
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001
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When
u2
u2
v2 =
1 2
=
5 1
.
Then P = [v1 v2 ] is an orthogonal m
momin (akm2466) HW02 gilbert (56780)
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001
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212 F, but it freezes at 0 C and boils at 100 C
on the Celcius
momin (akm2466) HW03 gilbert (56780)
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001
10.0 points
Equivalent linear systems have the same
solution set.
1
1. FAL
Version 064 FINAL gilbert (56780)
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001
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Find a basis for the Null space of the matrix
2 6 4 6
A = 1 3 3 4
Version 124 EXAM02 gilbert (57245)
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001
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Find a basis for the eigenspace of the matrix
1
3
3
A = 3 5 3 ,
sparks (cns658) HW05 gilbert (57245)
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002
3
4
.
+ x2
1
2
T
x1
x2
1
1
,
+ x2
2
2
= x1
3
.
1
determine
Version 040 EXAM03 gilbert (56780)
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001
1
x2
3.
2
10.0 points
x1
2
The vectors u1 and u2 shown in
x2
u2
2
2
4.
u1
2
Version 073 EXAM04 gilbert (56780)
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001
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If B = P DP 1 with P an orthogonal matrix and D a diagonal matri
Version 062 EXAM02 gilbert (56780)
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001
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The set
a + 2b
a b : a, b in R
H =
3b
is a subspace of R3 .
Tr
Question 06:
Answer:
Determine the number of kilogram of hydrogen per hour that passes through sheet
M
:
M JAt
DAt
C
x
Here the cross sectional area of sheet perpendicular to direction of diffusion is
coefficient is
Substitute
and
D
, elapsed diffusion t
Question 08:
A steel cantilever beam is used to carry a machine at its free end. To save weight, it is
proposed to replace the steel beam by an aluminum beam of identical dimensions. Find
the expected change in the natural frequency of the beam-machine sy
Question 09:
Determine the displacement, velocity, and acceleration of the mass of a spring-mass
&
system with and k = 500 N/m, m = 2 kg, x0 = 5 m/s., x0 = 0.1 m.
Answer:
Calculate the natural frequency n of a spring mass system as follows:
n
k
m
Here th
Question 5:
Air at a pressure of 6kN/m2 and a temperature of 3000C flows with a velocity 10m/s over a flat
plate 0.5m long. Estimate the cooling rate per unit width of the plate needed to maintain it at a
surface temperature of 270C.
Answer:
Air flow over
Question 04:
A
2 m 3m
flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces
along its 3 m long side. The free stream temperature and velocity of air are
total drag force acting on the plate is measured to be
0.86 N
20C
a
Question 03
The wall of a refrigerator is constructed of fiberglass insulation
sandwiched between two layers of 1-mm-thick sheet metal
space is maintained at
3C
surfaces of the wall are
averages
25C
C
k 0.035 W/m
C
k 15.1 W/m
. The refrigerated
, and
Question 02:
The surface temperature of a 3 in. diameter baked potato is observed to drop from
300F to 200F
in 5 min in an environment at
70F
. Determine the average heat transfer
coefficient between the potato and its surroundings. Using this heat transf
Question 01:
A 3mm diameter and 5 m long electric wire is tightly wrapped with a 2 mm thick plastic cover
whose thermal conductivity is
k 0.15 W/m K
. Electrical measurements indicate that a current
of 10 A passes through the wire and there is a voltage d
momin (akm2466) HW05 gilbert (56780)
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3
18
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=
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0
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001
10.0 points
Compute the expression AB BA when
0
3 1
A = 5 1 2
1
sparks (cns658) HW03 gilbert (57245)
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001
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Every matrix is row equivalent to a unique
matrix in echelon f
sparks (cns658) HW06 gilbert (57245)
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001
6
2
, B=
1
1
5
A=
3
with = d11 d22 d12 d21 , so
2
,
1
1
3
2
5
=
X=
10.0 po
Question 10:
The free-vibration response of a spring-mass system is observed to have a frequency of
2rad/s, an amplitude of 10 mm, and a phase shift of 1 rad from t = 0. Determine the initial
conditions that caused the free vibration. Assume the damping r