Let V be a finite-dimensional R-vector space. Let 3 and 3' be two ordered bases for V, and let Q = [[v], be the change of coordinate matrix in §2.5. We say that B and B' have the same orientation if det Q > 0; opposite orientations if det Q < 0. Show that when V = R", this definition is equivalent to the one given in the lectures.
Let V be a finite-dimensional R-vector space. Let 3 and 3' be two ordered bases for V, and let Q = [[v], be the change of coordinate matrix in §2.5. We say that B and B' have the same orientation if det Q > 0; opposite orientations if det Q < 0. Show that when V = R", this definition is equivalent to the one given in the lectures.
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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![6. Let V be a finite-dimensional R-vector space. Let ß and ß' be two ordered bases
for V, and let Q = [Iv], be the change of coordinate matrix in §2.5. We say that
B and B' have
the same orientation if det Q> 0;
opposite orientations if det Q < 0.
Show that when V = R", this definition is equivalent to the one given in the lectures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe72e13b-12e8-4646-917c-376e7356872c%2F7a87276d-cb2d-47d7-b3b7-b4ecb34aaf6d%2Fr01cwjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let V be a finite-dimensional R-vector space. Let ß and ß' be two ordered bases
for V, and let Q = [Iv], be the change of coordinate matrix in §2.5. We say that
B and B' have
the same orientation if det Q> 0;
opposite orientations if det Q < 0.
Show that when V = R", this definition is equivalent to the one given in the lectures.
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