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Name:Date:MATH 270: Linear Algebram270q032aPage 1 of 2CW 32: Vector Spaces 2In Problem 34, find a basis for each vector space.heen3α-2b]-4c a, b, c E RA.H =bB.K =|bE R3:a3b + 2c=useobrinIn Problem 35, define T: P2R2 byp(0)]T(p) = Ip(2)Find the standard matrix of the transformation. Show your calculations. (Note: thestandard basis for P2 is {1, t, t2}.)A.Find a basis for the kernel of the transformation. Show your calculations.B.

Question

Vector spaces 2 Pratice not test all of it 

Name:
Date:
MATH 270: Linear Algebra
m270q032a
Page 1 of 2
CW 32: Vector Spaces 2
In Problem 34, find a basis for each vector space.
heen
3α-2b]
-4c a, b, c E R
A.
H =
b
B.
K =|b
E R3:a
3b + 2c=
useobrin
In Problem 35, define T: P2R2 by
p(0)]
T(p) = Ip(2)
Find the standard matrix of the transformation. Show your calculations. (Note: the
standard basis for P2 is {1, t, t2}.)
A.
Find a basis for the kernel of the transformation. Show your calculations.
B.
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Name: Date: MATH 270: Linear Algebra m270q032a Page 1 of 2 CW 32: Vector Spaces 2 In Problem 34, find a basis for each vector space. heen 3α-2b] -4c a, b, c E R A. H = b B. K =|b E R3:a 3b + 2c= useobrin In Problem 35, define T: P2R2 by p(0)] T(p) = Ip(2) Find the standard matrix of the transformation. Show your calculations. (Note: the standard basis for P2 is {1, t, t2}.) A. Find a basis for the kernel of the transformation. Show your calculations. B.

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Step 1

35

A

Obtain the standard matrix of the transformation as follows.

Given that standard basis for P2 is {1, t, t2}.

Гр(о].
p(0)
1
т1):| p(2))
Р(2)
[Р(О1 Го
T()p(2)2
Р (2)
Tрe)- P(0)] Го
P(2) 4
Т
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Гр(о]. p(0) 1 т1):| p(2)) Р(2) [Р(О1 Го T()p(2)2 Р (2) Tрe)- P(0)] Го P(2) 4 Т

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Step 2

Answer:

The standard matrix of the transformation is

1 0 0]
1 2 4
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1 0 0] 1 2 4

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Step 3

B

Obtain the basis for the kernel of the transformation as follows.

Note that, the kernel of a linear transfo...

T(p) 0
P(0)]_[O
P(2)0
P(0) 0 andp(2) = 0
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T(p) 0 P(0)]_[O P(2)0 P(0) 0 andp(2) = 0

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