Suppose T: P3-M2,2 is a linear transformation whose action is defined by c+d b+d T(ax³ + bx²+cx+d)= 3a+d c+2d and that we have the ordered bases B=√x³, x², x, 1 D= for P3 and M2,2 respectively. 10 00 " 01 00 00 80] [18] [69] 00 10 01 a) Find the matrix of I corresponding to the ordered bases B and D. T is not one-to-one, T is not onto 000 MDB(T) = 0 0 0 000 b) Use this matrix to determine whether I is one-to-one or onto.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose T: P3→M2,2 is a linear transformation whose action is defined by
c+d_b+d
T(ax³ + bx²+cx+d)=
3a+d c+2d
and that we have the ordered bases
B ²= |x³, x²,
1| D=
x², x,
x, 1
for P3 and M₂.2 respectively.
10
01 00 00
00 00 10 01
"
7
"
a) Find the matrix of T corresponding to the ordered bases B and D.
000
MDB(T) = 0 0 0
000
b) Use this matrix to determine whether I is one-to-one or onto.
T is not one-to-one, T is not onto
Transcribed Image Text:Suppose T: P3→M2,2 is a linear transformation whose action is defined by c+d_b+d T(ax³ + bx²+cx+d)= 3a+d c+2d and that we have the ordered bases B ²= |x³, x², 1| D= x², x, x, 1 for P3 and M₂.2 respectively. 10 01 00 00 00 00 10 01 " 7 " a) Find the matrix of T corresponding to the ordered bases B and D. 000 MDB(T) = 0 0 0 000 b) Use this matrix to determine whether I is one-to-one or onto. T is not one-to-one, T is not onto
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