a. Find the transition matrix from C to B. T² = -21 [M]B = 5 -17 c. Find M. 0 -45 9 9 2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = -61 -36 -3 8 -3 -9 2 -3

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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www Consider the ordered bases B =
C
0
3
) for the vector space V of upper triangular 2 x 2 matrices.
-2
-2
-3
C = √²2² =²3²]·²2] [13
9
0
-1
0
a. Find the transition matrix from C to B.
T² =
[M]B =
-21
LO
M =
5
-17
c. Find M.
0
0
-45
9
9
-36
-3
8
-9
1
2
b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c =
-[-]
-2
18
-3
2
-3
1
0
-3
3
97² and
0
−1
0
1
-2
Transcribed Image Text:www Consider the ordered bases B = C 0 3 ) for the vector space V of upper triangular 2 x 2 matrices. -2 -2 -3 C = √²2² =²3²]·²2] [13 9 0 -1 0 a. Find the transition matrix from C to B. T² = [M]B = -21 LO M = 5 -17 c. Find M. 0 0 -45 9 9 -36 -3 8 -9 1 2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = -[-] -2 18 -3 2 -3 1 0 -3 3 97² and 0 −1 0 1 -2
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