Consider the ordered bases B = space V of upper triangular 2 x 2 matrices. a. Find the transition matrix from C to B. TB = [M]B = [²] =(3232) for the for the vector c. Find M. 2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = 4141 H M = and C= 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the ordered bases B =
space V of upper triangular 2 x 2 matrices.
a. Find the transition matrix from C to B.
TE=
[M]B =
-3
-2
[2][32]13²) nd=2²²2][32]
0
-1
c. Find M.
M =
0
-2
=
b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c =
0
C=
0
2
-1
-2
-3
-2
for the vector
Transcribed Image Text:Consider the ordered bases B = space V of upper triangular 2 x 2 matrices. a. Find the transition matrix from C to B. TE= [M]B = -3 -2 [2][32]13²) nd=2²²2][32] 0 -1 c. Find M. M = 0 -2 = b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = 0 C= 0 2 -1 -2 -3 -2 for the vector
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