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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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Question
Just answer 3c
![3. For each of the following linear operators T on a vector space V and
ordered bases 3, compute [T], and determine whether is a basis
consisting of eigenvectors of T.
(a) V=R²,- T (²) = (
a
(c) V=R³, Tb
B =
—
(b) V = P₁(R), T(a + bx) = (6a - 6b) + (12a − 11b)x, and
B = {3+4x, 2+3x}
с
10a-6b
17a - 10b
=
and B =
³= {()·()}
{0).(-)-0)}
1
3a + 2b 2c\
-4a-3b+2c, and
-c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32f77ee0-291c-46d0-b315-80fb2fd096d8%2F7a3e167c-a72d-4b26-9ac3-159cae00287b%2F277d6qp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. For each of the following linear operators T on a vector space V and
ordered bases 3, compute [T], and determine whether is a basis
consisting of eigenvectors of T.
(a) V=R²,- T (²) = (
a
(c) V=R³, Tb
B =
—
(b) V = P₁(R), T(a + bx) = (6a - 6b) + (12a − 11b)x, and
B = {3+4x, 2+3x}
с
10a-6b
17a - 10b
=
and B =
³= {()·()}
{0).(-)-0)}
1
3a + 2b 2c\
-4a-3b+2c, and
-c
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