Introduction to Matrix Algebra.pdf

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INTRODUCTIO;;
TO
MATRIX
ALGEBRA
SCHOOL
MATHE#ATlCS
STUDY
GROUP
R
YALE
UNIWRSCTY
?RESS
School
Mathematics
Study
Group
Introduction
to
Matrix
Algebra
Ii~troduction
Matrix
Algebra
to
Strrdetlt's
Text
Prcparcd
u n h r
t
~est~pen.kjon
h
of
rhc
Panel
on
Sample
T e x r h k s
of
rhc
School
Mathcmarm
Srudy
Group:
Frank
B.
Allen
Lyonr
Township
High
School
Edwirl
C.
Douglas
Donakl
E.
Richmond
Cllarlm
E,
Rickart
Hcnry
Swain
Robert
J.
Walkcr
Tafi
S C h I
Williamr
Collcgc
Yale
Univcrriry
New
Trier
Township
High
S c h d
Cornell
University
Ncw
Havcn
a d
h d o n ,
Y
a1c
University
Press
Coyyrig!lt
O
I*,
r p 5 r
by
Yak
Ut~jversiry.
Printed in
rhc
Ur~itcd
Starm
af
America.
A]]
r i ~ h t s
rescwcd.
Ths
h k
may
not
ltrc
repcduccd, in
whdc
o
in
part,
in
r
any
form,
wirho~~t
written
permission
from
the
publishen.
FinanciaZ
slspporr
for
the
S c b l
Mathemaria
Study
Group
has
km
providcd
by
rhe
Narional
Scicncu: Foundation.
The
i n c r e a s i n g
contribution
of
mathematics
to
the
culture of
the
d c r n
w r l d ,
as
well
as
i t s
importance
as
a
v i t a l
part
of
s c i e n t i f i c
and
humanistic
tdueation,
has
mndc
i t
essential
that
the
m a t h e ~ u t i e ai n
our
echool@
be
bath
wZ1
selected
and
e l l
taught.
t j i t h
t h i s
i n
mind,
the
various
mathc~atical
organLtaeions
i n
the
United
Seatss
cooperated
i n
the
forumtion
of
the
School
F ~ t k m a e i c sStudy
Group
(SPSC).
SMG
includes
college
and
unirersiley
mathmaticlans,
eencbera
of
m a t h w t i e s
a t
a l l
lavels,
experts
i n
education,
and
reprcscntarives
of
science
and
tcchrmlogy.
Pha
general
objective
o f
SMG
i a
the
i m p r o v m n t
a f
thc?
teaching
of
=themtics
in
the
sehmla
of
t h i s country.
The
l a t i o n u l
Science
Foundation
has
provided
subs
tantiaL
funds
for
the
support
of
this
endeavor.
One
of
the
pterequlsitea
for the
improvement
of
t h e
teaching
of
math&matira
in
our
~ c h m t si
e
on
improved
c u r r i e u ~ ~ n s
which takea account
of
thc
incrcas-
ing
use
of
oathematice
Ln
science
and
teehnoLogy
end i n
other
areas
o f
knowledge
and
a t
the
a m
timc
one
v f i i ~ h
ref
l o e t a
recent
advancta
i n
mathem~tica
i t s c l f .
One
of
thc
f l r n t
projects
undartaken
by
SrSC
was
t o
enlist
a
group
of
outstanding
mathematiclans
and
nrarhematica
teachern
t o
prepare
a
nariea
of
textbooks
uhich
would
illustrmre
such
A n
improved
curriculum.
The
professional
arathcmatLcLanlr
in
SMSG
belleve
that
the
mathematics
p r P
eented
In
this
t t x r
is
vaLuahLc
fat
a l l
w
l-ducatcd
2
citlzene
i n
our
society
t o
know
6nd
t h a t
it
ia
tqmrtant
f o r
the
prceollage
atudent:
to
learn
i n
prepara-
tion
far
advanced
vork
i n
thc f i e l d .
A t
thc
time
t i n e ,
teachers
in
SWC
believe
t h a t
it
is
presented
in
rrueh
a
farm
that
i t
can
ha
r ~ a d F l y
grasped
by
students.
In
most
inntanees
the
mnterlal
will
have
a
inmiltar
n o t e ,
h
the
prcsenta-
e
!
!
tion
and
the
point
of
vicv
vill
be
diftcrsnt.
Samc
matcrial w i l l
be
e n t i r e l y
neu
t o
ehc
traditional
curriculum,
This
i s
ar
i t
should
be,
for
~ A a t h c m & t i ~ &
ia
a
ltving and
an cvcwrawinff
subject, and
Rat
a
dead
and
frozen
product
of
an-
t i q u i t y .
This
heakthy
fusion
o f
the old
and
Ehc
ncu
should
lead
students
to
a
better
undcsstsnding
of
the
basic
concepts
and
structure
of
mthemtics
and
provide
a
f i m r
foundation for
understanding and
use
of
~ t h c m a t i c s
in
a
gcitntlfic
sociery.
n o t
intendad
that
this
book
be
regarded
an
the
mly
d c f i n i t l v a
way
of
presenting
good mathcmatica
t o
student#
a t
t h i s
Level.
Instead,
I t
should
be
thought
of
as e
ample
of
the
kind
of
i q r w e d
currieulua
that
we
need
and
as a
source
of
nuggestiana
for
the
authora
of
c-rclal
textbka.
It is
sincerely
hoped that
these
t e x t s
wLl1
lead
the
way
coward
inspiring
a
more
meaningful
reaching
o f
Hathemnckea,
t h e
Wcca
and
Servant
of
tho
Sctencea.
It
la

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