a) Find the matrix of T corresponding to the ordered bases B and D. Suppose T: M22 P3 is a linear transformation whose action is defined by a b = (a+d]x3 +(a+c+2d)x2 +[a+c+d]x+(a+b+d) %3D c d and that we have the ordered bases 1 0 B = 0 0 0 1 0 0 0 0 D= x3, x² , x, 1 0 1 0 0 1 0 for M2.2 and P3 respectively. a) Find the matrix of T corresponding to the ordered bases B and D. 100 1 1012 MDB(T) = %3D 1011 110 1 b) Use this matrix to determine whether T is one-to-one or onto. T is one-to-one, T is not onto
a) Find the matrix of T corresponding to the ordered bases B and D. Suppose T: M22 P3 is a linear transformation whose action is defined by a b = (a+d]x3 +(a+c+2d)x2 +[a+c+d]x+(a+b+d) %3D c d and that we have the ordered bases 1 0 B = 0 0 0 1 0 0 0 0 D= x3, x² , x, 1 0 1 0 0 1 0 for M2.2 and P3 respectively. a) Find the matrix of T corresponding to the ordered bases B and D. 100 1 1012 MDB(T) = %3D 1011 110 1 b) Use this matrix to determine whether T is one-to-one or onto. T is one-to-one, T is not onto
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How do you determine T is one-to-one or onto using the matrix.I need the detailed explanation and steps.Thank you.
![a) Find the matrix of T corresponding to the ordered bases B and D.
Suppose T: M2 2→P3 is a linear transformation whose action is defined by
a b
T
c d
= (a+d]x3 +{a+c+2d]x² +[a+c+d]x+[a+b+d)
and that we have the ordered bases
BB
1 0
0 1
0 0
0 0
x³ . x? , x 1
D =
3
%3D
0 0
0010
01
for M2.2 and P3 respectively.
a) Find the matrix of T corresponding to the ordered bases B and D.
1001
1012
MDB(T) =
1011
110 1
b) Use this matrix to determine whether T is one-to-one or onto.
T is one-to-one, T is not onto](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff56f00f-4be7-4511-bc7b-9683d0cff601%2Ff6008f8c-a72d-4c0b-b4e1-f8c13dea0373%2Fgsouo49_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Find the matrix of T corresponding to the ordered bases B and D.
Suppose T: M2 2→P3 is a linear transformation whose action is defined by
a b
T
c d
= (a+d]x3 +{a+c+2d]x² +[a+c+d]x+[a+b+d)
and that we have the ordered bases
BB
1 0
0 1
0 0
0 0
x³ . x? , x 1
D =
3
%3D
0 0
0010
01
for M2.2 and P3 respectively.
a) Find the matrix of T corresponding to the ordered bases B and D.
1001
1012
MDB(T) =
1011
110 1
b) Use this matrix to determine whether T is one-to-one or onto.
T is one-to-one, T is not onto
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