et B = and C = {c1,c2} be bases for a vector space V, and suppose b, = 8c, - 5c2 and b2 = - 7c, + 9c2. Find the change-of-coordinates matrix from B to C. Find [x]c for x= - 6b, +4b2. Use part (a). 8 -7 P = C+B - 5 [x]c = Simplify your answer.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 6E
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Let B =
{b1.b2} and C =
be bases for a vector space V, and suppose b, = 8c, - 5c2 and b2 = - 7c1 + 9c2.
%3D
a. Find the change-of-coordinates matrix from B to C.
b. Find [x]c for x = - 6b, +4b2. Use part (a).
8 -7
а.
P
C-B
- 5
b. [x]c
(Simplify your answer.)
II
Transcribed Image Text:Let B = {b1.b2} and C = be bases for a vector space V, and suppose b, = 8c, - 5c2 and b2 = - 7c1 + 9c2. %3D a. Find the change-of-coordinates matrix from B to C. b. Find [x]c for x = - 6b, +4b2. Use part (a). 8 -7 а. P C-B - 5 b. [x]c (Simplify your answer.) II
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