Let T: M2x2 → P₂ be defined by T A) A basis for the image (range) of T would be: {[][]} O{1, 1, 1, 2²} {[33]} o{0} O{1, x, x²} Ⓒ{1, 2²} {[89]} B) A basis for the kernel of T would be: {[3]} o {0} {[89]} O{1, ²} O{1, 1, 1, ²} {} =a+b+c+dx².
Let T: M2x2 → P₂ be defined by T A) A basis for the image (range) of T would be: {[][]} O{1, 1, 1, 2²} {[33]} o{0} O{1, x, x²} Ⓒ{1, 2²} {[89]} B) A basis for the kernel of T would be: {[3]} o {0} {[89]} O{1, ²} O{1, 1, 1, ²} {} =a+b+c+dx².
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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![Let T: M2x2 P2 be defined by T
A) A basis for the image (range) of T would be:
#3
{[(4)
O{1, 1, 1, ²}
{[3]}
o{0}
O {1, x, x²}
Ⓒ{1, ²}
E
{[89]}
O
B) A basis for the kernel of T would be:
{[2,3]}
{0}
{[%]}
O {1, ²}
O {1, 1, 1, x²}
Ⓒ{1, x, x²}
O
O
{[3][48]}
4
([a b]) =
с
R
%
G Search or type URL
5
T
=a+b+c+dx².
A
6
Y
&
7
D
8
(
O
)
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa79c18d0-6a0e-4a38-9496-04f82bd62d69%2F49c63620-1c5f-4cca-ac81-00aef869d865%2Fxgbwmyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T: M2x2 P2 be defined by T
A) A basis for the image (range) of T would be:
#3
{[(4)
O{1, 1, 1, ²}
{[3]}
o{0}
O {1, x, x²}
Ⓒ{1, ²}
E
{[89]}
O
B) A basis for the kernel of T would be:
{[2,3]}
{0}
{[%]}
O {1, ²}
O {1, 1, 1, x²}
Ⓒ{1, x, x²}
O
O
{[3][48]}
4
([a b]) =
с
R
%
G Search or type URL
5
T
=a+b+c+dx².
A
6
Y
&
7
D
8
(
O
)
0
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