0 Let 2: 1R² → 112³ be given by L Find a می ([*]) = [ basis for Also be the 3 2 2 line ar 3 }{][ operato 24 x2 23) 3 Ker (L) and verify the dimension a bas
0 Let 2: 1R² → 112³ be given by L Find a می ([*]) = [ basis for Also be the 3 2 2 line ar 3 }{][ operato 24 x2 23) 3 Ker (L) and verify the dimension a bas
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
Related questions
Question
![determine
Using
rank of A,
the homogeneous system
a non-trivial
salution
or not.
Ax=o
whether
has
(4) Suppose L: IR³ → IR³ is a
operator and
L ( [0,1,0]) = [5,-1,3],
L( [0,0,1]) = [-4, 0, -2].
find
and
is a linear
L ( [1,0,0]) = [-3, 2, 4],
L[[x, y, 2]) for any [x,y, 2] E1³
also find L([6,2₁-7]).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a984aa7-cbc1-4731-8b36-d2d2c29ad46b%2F6fdc41bc-e00c-4656-a8a7-2fe996d64d76%2Fjbnc2gu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:determine
Using
rank of A,
the homogeneous system
a non-trivial
salution
or not.
Ax=o
whether
has
(4) Suppose L: IR³ → IR³ is a
operator and
L ( [0,1,0]) = [5,-1,3],
L( [0,0,1]) = [-4, 0, -2].
find
and
is a linear
L ( [1,0,0]) = [-3, 2, 4],
L[[x, y, 2]) for any [x,y, 2] E1³
also find L([6,2₁-7]).
![12
3
Let
given by
Show
given
is
2:1R ² → 1R ³ be
(A) [
that
an
می
3
find a
basis for KerlL)
for range(L). Also, verity
theorem.
a
A =
the
of degree
degree $2.
Consider
the
be the
[
3
isomorphism
vector space of
2
2
2
by
L (p(x)) = p(x) + p'(x)
1
matrix
2
-)
-4
line or operator
2
- 3
5
mapping L: P₂ → P₂
-)
][
24
and
the dimension
3
3
212
×3]
a
basi
where P₂ is
all polynomials](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a984aa7-cbc1-4731-8b36-d2d2c29ad46b%2F6fdc41bc-e00c-4656-a8a7-2fe996d64d76%2Faf89wun_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12
3
Let
given by
Show
given
is
2:1R ² → 1R ³ be
(A) [
that
an
می
3
find a
basis for KerlL)
for range(L). Also, verity
theorem.
a
A =
the
of degree
degree $2.
Consider
the
be the
[
3
isomorphism
vector space of
2
2
2
by
L (p(x)) = p(x) + p'(x)
1
matrix
2
-)
-4
line or operator
2
- 3
5
mapping L: P₂ → P₂
-)
][
24
and
the dimension
3
3
212
×3]
a
basi
where P₂ is
all polynomials
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