Recall that M2,2 is the vector space of real 2 x 2-matrices and P3 is the vector space of real polynomials of degree at most 3. Let T : M₂,2 P3 be a linear function satisfying Find the following: ( (a) T (b) T (c) T (d) T (e) T 1 0 0 1 C −1 1 = || || → T ([1]) = T + ( [i !]) = = -4, T([:]) = -4x², T = -x - 3, ([i]). = = 3x³ - 4x.
Recall that M2,2 is the vector space of real 2 x 2-matrices and P3 is the vector space of real polynomials of degree at most 3. Let T : M₂,2 P3 be a linear function satisfying Find the following: ( (a) T (b) T (c) T (d) T (e) T 1 0 0 1 C −1 1 = || || → T ([1]) = T + ( [i !]) = = -4, T([:]) = -4x², T = -x - 3, ([i]). = = 3x³ - 4x.
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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![Recall that M2,2 is the vector space of real 2 x 2-matrices and P3 is the vector space of real polynomials of
degree at most 3. Let T: M2,2 → P3 be a linear function satisfying
Find the following:
( [
([
(a) T
(b) T
(c) T
(d) T
(e) T
1
00
00
00
1
=
=
(12 7³])
=
1
7(D)--+
= -4,
T
0
T
( )=-*- 3.
3,
T([i])=-4x². T([8])=3x² - 4x
:
:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6312c2ba-3ddd-4e1a-91e2-a12af60ced38%2F83672a7c-2375-4a9f-a372-7f3c8f8557f5%2Fg4ilmy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Recall that M2,2 is the vector space of real 2 x 2-matrices and P3 is the vector space of real polynomials of
degree at most 3. Let T: M2,2 → P3 be a linear function satisfying
Find the following:
( [
([
(a) T
(b) T
(c) T
(d) T
(e) T
1
00
00
00
1
=
=
(12 7³])
=
1
7(D)--+
= -4,
T
0
T
( )=-*- 3.
3,
T([i])=-4x². T([8])=3x² - 4x
:
:
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