Suppose T: P3-M2,2 is a linear transformation whose action is defined by a+3c a+3c-2d T(ax3 +bx²+cx+d) = 3c-2d 3b+3c and that we have the ordered bases 10 0 ¹ D= [] [] [] [] " 00 00 10 01 B = x³, x² X, 1 for P3 and M₂,2 respectively. a) Find the matrix of I corresponding to the ordered bases B and D. 000 MDB(T) = 0 0 0 000 b) Use this matrix to determine whether T is one-to-one or onto. T is one-to-one, T is onto
Suppose T: P3-M2,2 is a linear transformation whose action is defined by a+3c a+3c-2d T(ax3 +bx²+cx+d) = 3c-2d 3b+3c and that we have the ordered bases 10 0 ¹ D= [] [] [] [] " 00 00 10 01 B = x³, x² X, 1 for P3 and M₂,2 respectively. a) Find the matrix of I corresponding to the ordered bases B and D. 000 MDB(T) = 0 0 0 000 b) Use this matrix to determine whether T is one-to-one or onto. T is one-to-one, T is onto
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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![Suppose T: P3-M2.2 is a linear transformation whose action is defined by
T(ax³ + bx²+cx+d) =
a+3c a+3c-2d
3c-2d 3b+3c
and that we have the ordered bases
x³, x² X, 1 D=
B 3
=
"
for P3 and M2,2 respectively.
01
00
[366]
00
10
10
T is one-to-one, T is onto
00
a) Find the matrix of I corresponding to the ordered bases B and D.
0 0 0
MDB(T) = 0 0 0
000
b) Use this matrix to determine whether I is one-to-one or onto.
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F373110e7-e385-4127-adf5-b0ae0e197db9%2Fbb70dc2c-6114-4a7d-ba9e-7582f81f5c94%2Fk85mra_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose T: P3-M2.2 is a linear transformation whose action is defined by
T(ax³ + bx²+cx+d) =
a+3c a+3c-2d
3c-2d 3b+3c
and that we have the ordered bases
x³, x² X, 1 D=
B 3
=
"
for P3 and M2,2 respectively.
01
00
[366]
00
10
10
T is one-to-one, T is onto
00
a) Find the matrix of I corresponding to the ordered bases B and D.
0 0 0
MDB(T) = 0 0 0
000
b) Use this matrix to determine whether I is one-to-one or onto.
0
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