Ground Lesson 10.4
Subject: Ignition system
Attention: Ok, so the electrical system fails? Does the engine quit as well?
Motivation: No, the ignition system is independent from the helicopters electrical system, thats why we can
continue to fly.
Overview:
Ground Lesson 10.2
Subject: Flight controls
Overview:
Control lift and thrust
Collective
Cyclic
Throttle
Pedals
Trim and friction systems
Equipment:
Recommended literature: HPM 22, RFH 41, POH 74
Control lift and thrust
Collective pitch control

Funct
Ground Lesson 10.6
Subject:
Fuel System
Introduction/Objective:
The student will be introduced to the helicopters fuel system
Attention:
Compared to a car, the helicopter just dont stop at the side of the road if we run
out of fuel.
Motivation:
It is ther
Ground Lesson 10.5
Subject: Aircraft lights
Overview:
Navigation / Position
Anti collision
Landing lights
Interior lights
Navigation / Position lights


Three colored lights positioned around the helicopter
o Red position light on left side of fuselage
Ground Lesson 10.3
Subject:
Electrical system R22
Introduction:
Basic overview of the electrical system in the R22. Use of main components.
Attention:
How would a city work without electrical power?
Motivation:
So can we fly without the electrical system
Ground Lesson 10.11
Subject: Engine instruments
Overview:
Engine gauges
Recommended literature: POH, HPM
Cylinder head temperature

POH 29
Displays a direct temperature reading
From one of the cylinder heads
Green arc 200 F 500 F (93C  260C)
Red line 
Ground Lesson 10.10
Subject: Oil and Oil system
Overview:
Oil and oil system
Gauges
Warning lights
Oil system operation
Hydraulic systems
Equipment:
Recommended literature:
Oil and oil system




The oil system cools and lubricates the engine
Reducing
Ground Lesson 10.7
Subject: Induction system
Attention: Can we just send in some fuel and some air into the engine, and all will be good?
Motivation: No, it needs to be accurately mixed for a optimized combustion. This is todays topic.
Overview: This less
always yes. The proof is not difficult. Take a
vector u and w such that u U W 3 w. This
means that both u and w are in both U and W.
But, since U is a vector space, u + w is also
in U. Similarly, u + w W. Hence u + w
U W. So closure holds in U W and this
What is the probability that the columns of M
form a basis for B3 ? (Hint: what is the
relationship between the kernel of M and its
eigenvalues?) Note: We could ask the same
question for real vectors: If I choose a real
vector at random, what is the proba
18 19 20 21 22 23 24 25 . Now test
your skills on det 1 2 3 n n + 1 n +
2 n + 3 2n 2n + 1 2n + 2 2n + 3 3n . . . . . . . . .
n2n+1n2n+2n2n+3n2
. Make sure to jot down a few brief
notes explaining any clever tricks you use. 6.
For which values of a does U
How many different linear transformations did
you find? Compare your answer to part (c). (g)
Suppose L1 : B3 B and L2 : B3 B are linear
transformations, and and are bits. Define a
new map (L1 + L2) : B3 B by (L1 + L2)(v)
= L1(v) + L2(v). Is this map a lin
Decomposition 309 Thus LL : W W and L
L : V V and both have eigenvalue
problems. Moreover, as is shown in Chapter
15, both L L and LL have orthonormal
bases of eigenvectors, and both MMT and
MTM can be diagonalized. Next, let us make a
simplifying assumpt
exactly to that same point after one orbit of
the earth. Unfortunately, if there is a small
mistake in the original location of the satellite,
which the engineers label by a vector X in R 3
with origin1 at O, 1This is a spy satellite. The
exact location o
that the matrix on the left hand side must be
invertible, so we examine its determinant det
1 4 10 4 5 7 3 0 h + 3 = 4 (4 (h +
3) 7 3) + 5 (1 (h + 3) 10 3) = 11(h 3)
Hence we obtain a basis whenever h 6= 3. 339
340 Sample Second Midterm 340 F Sample
Fina
, 0 1 0 , 1 2 0 1 2 .
The new matrix M0 of the linear
transformation given by M with respect to the
bases O and O0 is M0 = 1 0 0 2 0 0 , so
the singular values are 1, 2. Finally note that
arranging the column vectors of O and O0 into
change of basis matri
bc . (a) For which values of det M does M have
an inverse? (b) Write down all 22 bit matrices
with determinant 1. (Remember bits are either
0 or 1 and 1 + 1 = 0.) (c) Write down all 2 2
bit matrices with determinant 0. (d) Use one of
the above examples to
x z + 2w = 1 x + y + z w = 2
y 2z + 3w = 3 5x + 2y z + 4w = 1 (a) Write
an augmented matrix for this system. (b) Use
elementary row operations to find its reduced
row echelon form. (c) Write the solution set
for the system in the form S = cfw_X0 + X i i
GramSchmidt algorithm in terms of projection
matrices. 4. Show that if v1, . . . , vk are
linearly independent that the matrix M = (v1
vk) is not necessarily invertible but the matrix
MTM is invertible. 5. Write out the singular
value decomposition the
spancfw_L(u1), . . . , L(uq). Now we show that
cfw_L(u1), . . . , L(uq) is linearly independent. We
argue by contradiction. Suppose there exist
constants d j (not all zero) such that 0 = d
1L(u1) + + d qL(uq) = L(d 1u1 + + d quq).
But since the u j are li
on the right and one going around the outside
of the circuit). Respectively, they give the
equations 60 I 80 3I = 0 80 + 2J V + 3J =
0 60 I + 2J V + 3J 3I = 0 . (F.1) The above
equations are easily solved (either using an
augmented matrix and row reducing
M3. Multiplication is commutative a b = b a.
M4. There exists a multiplicative inverse a 1 if
a 6= 0. D. The distributive law holds a (b + c) =
ab + ac. Roughly, all of the above mean that
you have notions of +, , and just as for
regular real numbers. Fie
was not quite sure whether the statistician
was pulling his leg. How can you know that?
was his query. And what is this symbol here?
Oh, said the statistician, this is . And
what is that? The ratio of the circumference
of the circle to its diameter. Well,
your answer to part (a) in the form Y TMY = g.
Make sure you give formulas for the new
unknown column vector Y and constant g in
terms of X, M, C and f. You need not multiply
out any of the matrix expressions you find. If
all has gone well, you have found
Suppose that L is bijective (i.e., onetoone and
onto). i. Show that dim V = rankL = dim W. ii.
Show that 0 is not an eigenvalue of M. iii.
Show that M is an invertible matrix. (b) Now,
suppose that M is an invertible matrix. i. Show
that 0 is not an eig