9 Advantages of a Yector Space. Vector Space is set objects which soie Some properties, Once we get a Vector space of objects. "The structural Objects iwe can perform different operations similarities of can be observed. One can define inner product more properties. vector space to get on that non-linear 8) It can be observe boundary value problems fall outside the field of linear spaces L' is called a, b EL Linear Space A set linear if for all space, get, xa + pb €L we where constants are To show non-linear bounday value problem fall outside the field of linear space ASUME find the counter example
9 Advantages of a Yector Space. Vector Space is set objects which soie Some properties, Once we get a Vector space of objects. "The structural Objects iwe can perform different operations similarities of can be observed. One can define inner product more properties. vector space to get on that non-linear 8) It can be observe boundary value problems fall outside the field of linear spaces L' is called a, b EL Linear Space A set linear if for all space, get, xa + pb €L we where constants are To show non-linear bounday value problem fall outside the field of linear space ASUME find the counter example
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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i need this in words
not handwritten
please Rewrite this
Transcribed Image Text:Space is set objects · which Betisfi
Advantages of
a Yector Space .
Vector Space is set objects which sot
Some properties Once we get a Vector
space , we can perform different operations
of
of objects. " The structural similarities
One can define
get
Objects
can be
observed.
ioner product
vector space
to
on
more
properties .
that
non-linear
It can be
observe
boundary value problems all outside the
linear spaces.
field of
Linear Space
L'
is called
A set
linear
if
for
all
a, b 6L
space,
get,
xa + B b E L.:
we
are
constants
where
To show
non-linear
boundary value problem
fall outside the field
of linear
space
essume findl the counter example
Transcribed Image Text:) what makes a set of objeds
a vector space ?
Let
A
must satisty
is
set
of objects . It
following properties.
Take
two objects
and v
from
set A
i) The
of
u and
denoted. by
Sum
V
is in A
U +V
(u+v) +w =
u+(v+w)
iv) There
is a
Zero vector
O in A
such that
Uto =4
) For
each
u in A.
there is a' vector
-u in A
such that,
u+ (-u)
こ6
c denoted
Vi) The scalar
by cu
multiple of u by
I is in A
Vii)
c.Cu+v)
= CutCV
Viii)
(Ct d) u =
củ + du
ix)
c (du)
(ed)u
14 = 4
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