4. Given two bases (b) = (b1, b2) and (f) = (fi, f2) of R?. Let Af be a matrix of a lineartransformation y : R? → R² with respect to the basis (f) and let X, be a coordinatevector of a vector X E R² with respect to (6).A, - (;). -(:). -(1). -()-(:).3fi2f2 =3b2-3Af1 3Calculate• the coordinate vector of X with respect to the basis (f).• the coordinate vector of p(X) with respect to the basis (b).

Given two bases b=b1,b2 and f=f1,f2 of ℝ2 where b1=12, b2=34, f1=11, f2=23 Let Af be a matrix of a…

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

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

4. Given two bases (b) = (b1, b2) and (f) = (fi, f2) of R?. Let Af be a matrix of a linear
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 (6).
A, - (;). -(:). -(1). -()
-(:).
3
fi
2
f2 =
3
b2
-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 (b).

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