-3 0] 0 3 -3 0 C = for the vector space V -2 3 -5 of lower triangular 2 x 2 matrices with zero trace. 0 •{(a d): a +d=0}. a. Find the change of basis matrix from C to B. B = That is, V = PBC = [M]B 0 -4 0 -1 01 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C'is [M]c = [1¹] c. Find M. -88 M = and

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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Consider the ordered bases
-3 01 0
01
B =
That is, V
PBC =
0 3
-3
0
C =
for the vector space V
-2 3 -5
-5 1
of lower triangular 2 x 2 matrices with zero trace.
0
= {(²₂9): a +d=0}.
d
a. Find the change of basis matrix from C to B.
[M]B
=
M =
b. Find the coordinates of Min the ordered basis B if
the coordinate vector of M in C'is [Mc = [¹]
[-1
-1
18
c. Find M.
0
0
and
Transcribed Image Text:Consider the ordered bases -3 01 0 01 B = That is, V PBC = 0 3 -3 0 C = for the vector space V -2 3 -5 -5 1 of lower triangular 2 x 2 matrices with zero trace. 0 = {(²₂9): a +d=0}. d a. Find the change of basis matrix from C to B. [M]B = M = b. Find the coordinates of Min the ordered basis B if the coordinate vector of M in C'is [Mc = [¹] [-1 -1 18 c. Find M. 0 0 and
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