Let A = fa,,a2,a3} and B={b1.b2,b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 = - b, + b2 + bg, az = b2 - 4b3a. Find the change-of-coordinates matrix from A to B.b. Find [x], for x = 3a, + 4a, + az5- 1a. PB+A1.1 - 4b. [x]R =(Simplify your answers.)DDD

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Let A= {a1,a2,a3} and B= {b1,b2 b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 = -b, +b2 + b3, az = b2 – 4b3. a. Find the change-of-coordinates matrix from A to B. b. Find [x], for x= 3a, + 4a, + az. 5 - 1

Let A= {a1,a2,a3} and B= {b1,b2 b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 = -b, +b2 + b3, az = b2 – 4b3. a. Find the change-of-coordinates matrix from A to B. b. Find [x], for x= 3a, + 4a, + az. 5 - 1

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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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let A = fa,,a2,a3} and B=
{b1.b2,b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 = - b, + b2 + bg, az = b2 - 4b3
a. Find the change-of-coordinates matrix from A to B.
b. Find [x], for x = 3a, + 4a, + az
5
- 1
a. P
B+A
1.
1 - 4
b. [x]R =
(Simplify your answers.)
DDD

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