4. Given two bases (b) = (b1, b2) and (f)transformation y : R? → R² with respect to the basis (f) and let X be a coordinatevector of a vector X E R² with respect to (b).(f1, f2) of R?. Let Af be a matrix of a linearh- (}). -(1) -(1) -()A; - (1) x-()3b2 =42f2 =3Af =1 3Calculate• the coordinate vector of X with respect to the basis (f).• the coordinate vector of p(X) with respect to the basis (6).

Given that (b) =b1, b2 and f=f1, f2 are two bases of ℝ2. Af is a matrix of a linear transformation φ…

4. Given two bases (b) = (b1, b2) and (f) = (fi, f2) of R². Let Af be a matrix of a linear transformation p : R? + R² with respect to the basis (f) and let X, be a coordinate vector of a vector X E R? with respect to (b). -(:). -(:). -(1). 4-() by = (;) h-(;) fi 3 Ay -(). x-() -1 2 1 3 Calculate • the coordinate vector of X with respect to the basis (f). • the coordinate vector of (X) with respect to the basis (b).

4. Given two bases (b) = (b1, b2) and (f) = (fi, f2) of R². Let Af be a matrix of a linear transformation p : R? + R² with respect to the basis (f) and let X, be a coordinate vector of a vector X E R? with respect to (b). -(:). -(:). -(1). 4-() by = (;) h-(;) fi 3 Ay -(). x-() -1 2 1 3 Calculate • the coordinate vector of X with respect to the basis (f). • the coordinate vector of (X) with respect to the basis (b).

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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Linear Algebra

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

4. Given two bases (b) = (b1, b2) and (f)
transformation y : R? → R² with respect to the basis (f) and let X be a coordinate
vector of a vector X E R² with respect to (b).
(f1, f2) of R?. Let Af be a matrix of a linear
h- (}). -(1) -(1) -()
A; - (1) x-()
3
b2 =
4
2
f2 =
3
Af =
1 3
Calculate
• the coordinate vector of X with respect to the basis (f).
• the coordinate vector of p(X) with respect to the basis (6).

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