Consider the ordered bases B = and C = { [ 7³ 1 PBC 3-5 of lower triangular 2 × 2 matrices with zero trace. That is, V = {(ag):a+d=0}. a. Find the change of basis matrix from C to B. 0 = [M]B -30] [5 [00] b. Find the coordinates of M in the ordered basis B if the 2 coordinate vector of M in C'is [M]c = [²] 18 c. Find M. M = -2 {[3² 1 [21]} 0 2 -4 for the vector space V
Consider the ordered bases B = and C = { [ 7³ 1 PBC 3-5 of lower triangular 2 × 2 matrices with zero trace. That is, V = {(ag):a+d=0}. a. Find the change of basis matrix from C to B. 0 = [M]B -30] [5 [00] b. Find the coordinates of M in the ordered basis B if the 2 coordinate vector of M in C'is [M]c = [²] 18 c. Find M. M = -2 {[3² 1 [21]} 0 2 -4 for the vector space V
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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Question
![Consider the ordered bases B
=
and C
{[7³
-30] [5
3
1
of lower triangular 2 x 2 matrices with zero trace.
That is, V = {(a): a+d=
1=0}.
a. Find the change of basis matrix from C to B.
188
[00]
PBC=
b. Find the coordinates of M in the ordered basis B if the
coordinate vector of M in C' is [M]c = [2]
[M]B
-2 0] 0
{[3² 9] [248]}
0 2 -4
for the vector space V
-
c. Find M.
M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbd5786d-c03d-4368-809a-5f6317a6d7c8%2Ff50b3cbe-0bc2-47d2-8e85-b5bcbacead57%2Fsb8awdb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the ordered bases B
=
and C
{[7³
-30] [5
3
1
of lower triangular 2 x 2 matrices with zero trace.
That is, V = {(a): a+d=
1=0}.
a. Find the change of basis matrix from C to B.
188
[00]
PBC=
b. Find the coordinates of M in the ordered basis B if the
coordinate vector of M in C' is [M]c = [2]
[M]B
-2 0] 0
{[3² 9] [248]}
0 2 -4
for the vector space V
-
c. Find M.
M
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