Jump to level1 (E)-E (:). {} H} 2x2 4 B = x1 Let T : R² → R² be defined by T . Let u = and x2 2x1 – 2x2 C = Given Pc = -2 use the Fundamental Theorem of Matrix Representations to find [T] (Pg(u)). 3

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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Jump to level 1
- 2x2
2x1 – 2x2
{{]-H}-
-x1
Let T : R
→ R² be defined by T
Let u =
B =
and
x2
3
C =
1
-1
use the Fundamental Theorem of Matrix Representations to find [T](PB(u)).
3
Given Pc
-2
Ex: 5
(TE(Ps (u)) =
Transcribed Image Text:Jump to level 1 - 2x2 2x1 – 2x2 {{]-H}- -x1 Let T : R → R² be defined by T Let u = B = and x2 3 C = 1 -1 use the Fundamental Theorem of Matrix Representations to find [T](PB(u)). 3 Given Pc -2 Ex: 5 (TE(Ps (u)) =
Expert Solution
Step 1

Step:-1

According to Fundamental Theorem of Matrix Representation:-

TBC PB u  =PC Tu,  u2  -------(1)

Now, given that 

T x1x2  =-x1 -2x22x1 -2x2

u=4-2,  Pc =1-1-23

Step:-2

Tu =T 4-2  =-4-2-224-2-2=-4+48+4Tu =012

Step:-3

Using above result (1), we have

TBC PB u  =PC TuTBC PB u  = 1-1-23 012 =-1236TBC PB u   =-1236

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