direction at 0.98c in the laboratory frame. Find (c) the
acceleration as
measured in the laboratory, and (d) the angle the
acceleration makes
with the x axis in the laboratory frame. [(a) 5 cm/sec2 (b
W_ .IHIJ JIII MIIIlJIJ4mJI
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o /
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M Ila IWIIIII
_ IIWIII . 1y
M J lb a
WW m .J _ m.m AM P
A (M M .*
, y : mi 
, J Hi. Ilw I r "I II I R IN
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MMIIU I m%w_ a I II I; mm mm . I mm
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AM; V 3333.111
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, t: 1".e P a a. e 8
1% w a 'ul Mr IV) rIT L
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dx'
Since we have set ourselves the limitation that V'a: = dt' =
0, the
preceding equation becomes
dt = y dt'. (29.3)
Dividing each of Eqs. 29.2 by 29.3, we obtain the
transformation
equations for
cube passes the origin by a distant observer located along
the y axis.
At what angle with respect to V would a photographer in
the proper
frame have to be located to take the same picture? [127]
(29
and .  Mesons," Phys. Rev. 88, 179 (1952).
D. H. Frisch and J. H. Smith, "Measurement of
Relativistic Time Dilation
Using p. Mesons," Am. J. Phys. 31, 342 (1963).
D. H. Frisch, J. H. Smith, and F. L.
need in this book for the more general equations of
transformation
which could be derived from Eqs. 29.1.
In the Galilean transformation the acceleration of a
particle
is the same in all inertial fra
event takes place in the time interval during which the
shell
passes, information about the event is swept along by the
shell
and will be recorded by the camera.
In spite of inferences that might be d
circular, the moon was bounded by circles, the planets
were circular,
and the stars seemed to describe circular paths. On the
surface of the earth, and for horizontal motions, a state of
rest
seemed t
Math 260
Assignment #3
Spring 2011
In order to receive full marks, students must indicate the various steps taken.
1. Find the inverse of
1 2 3
(a) A = 2 5 3
1 0 8
1 0
2. Let A = 2 4
3 1
the following
Math 260
Assignment #1
Spring 2011
1. Solve the following matrix equation for a, b, c and d.
a b
c 3d d
=
c d
2a + d a + b
3 0
1 5 2
4
1
1
4
2
2. Consider the matrices A = 1 2 , B =
, C =
, D = 1 0
Math 260
Assignment #2
Spring 2011
1. Which of the following are linear equations in x1 , x2 and x3 . If not, why?
2
5
(a) 2x1 x2 + 5x3 = 1
(e) x2 = 3x1 +
x3
5
3
1/5
1/7
k
(b) x1 x2 + 3 x3 = 8
(f ) 2
MATH 260 BASIC LINEAR ALGEBRA
Answers to Problem Set 2 (Systems of linear equations)
1. (i) System is inconsistent, since [
] [
2. (i)
(ii) Consider as a parameter. System is consistent if
[ ]
[ ]
[

MATH 260 BASIC LINEAR ALGEBRA
Answers to Problem set 3 (Determinants)
1
1. (Ex. 3, p. 117) Given that
a
1 1
a
(i)
x2
2
b 4 , calculate the following determinants
2 3b
(ii)
(iii)
(iv)
x
x
1
b 4x
ax
2
3
MATH 260 BASIC LINEAR ALGEBRA
Problem set 4 (Vector Spaces)
under which (
1. Find the conditions on
2. Show that vectors (
)(
)(
)
(
6. Find
cfw_(
(
and
)(
)(
defined on
1 0 2 1 1 2
,
,
.
1 1 2 2 2
Math 260
Assignment #1
Spring 2011
1. Solve the following matrix equation for a, b, c and d.
a b
c 3d d
=
c d
2a + d a + b
Solution: The matrix equation gives the following linear system:
a
b
c
d
=
MATH 260 BASIC LINEAR ALGEBRA
Problem set 6 I. Diagonalization, eigenvalues, eigenvectors. Diagonalization of real symmetric matrices
1. Find the characteristic polynomial, the eigenvalues, and
corres
Canan Bozkaya
Math 260
Assignment #2 & Solutions
Spring 2011
In order to receive full marks, students must indicate the various steps taken.
1. Which of the following are linear equations in x1 , x2 a