1-The set B={3−2x^2, 6−3x−4x^2, 6x−20+14x^2} is a basis for P2. Find the coordinates of p(x)=45−15x−32x^2 prelative to this basis: [p(x)]B= 2- Let f:ℝ2→ℝf:R2→R be defined by f(⟨x,y⟩)=6x+5yf(⟨x,y⟩)=6x+5y. Is ff a linear transformation? a. f(⟨x1,y1⟩+⟨x2,y2⟩)=? (Enter x1x1 as ??x1, etc.) f(⟨x1,y1⟩)+f(⟨x2,y2⟩)= ? Does f(⟨x1,y1⟩+⟨x2,y2⟩)=f(⟨x1,y1⟩)+f(⟨x2,y2⟩) for all ⟨x1,y1⟩,⟨x2,y2⟩∈ℝ^2? b- f(c⟨x,y⟩)= c(f(⟨x,y⟩))= Does f(c⟨x,y⟩)=c(f(⟨x,y⟩)) for all c∈ℝ and all ⟨x,y⟩∈ℝ2 c-Is f a linear transformation?
1-The set B={3−2x^2, 6−3x−4x^2, 6x−20+14x^2} is a basis for P2. Find the coordinates of p(x)=45−15x−32x^2 prelative to this basis: [p(x)]B= 2- Let f:ℝ2→ℝf:R2→R be defined by f(⟨x,y⟩)=6x+5yf(⟨x,y⟩)=6x+5y. Is ff a linear transformation? a. f(⟨x1,y1⟩+⟨x2,y2⟩)=? (Enter x1x1 as ??x1, etc.) f(⟨x1,y1⟩)+f(⟨x2,y2⟩)= ? Does f(⟨x1,y1⟩+⟨x2,y2⟩)=f(⟨x1,y1⟩)+f(⟨x2,y2⟩) for all ⟨x1,y1⟩,⟨x2,y2⟩∈ℝ^2? b- f(c⟨x,y⟩)= c(f(⟨x,y⟩))= Does f(c⟨x,y⟩)=c(f(⟨x,y⟩)) for all c∈ℝ and all ⟨x,y⟩∈ℝ2 c-Is f a linear transformation?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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1-The set B={3−2x^2, 6−3x−4x^2, 6x−20+14x^2} is a basis for P2. Find the coordinates of p(x)=45−15x−32x^2 prelative to this basis:
[p(x)]B=
2-
Let f:ℝ2→ℝf:R2→R be defined by f(⟨x,y⟩)=6x+5yf(⟨x,y⟩)=6x+5y. Is ff a linear transformation?
a.
f(⟨x1,y1⟩+⟨x2,y2⟩)=?
(Enter x1x1 as ??x1, etc.)
f(⟨x1,y1⟩)+f(⟨x2,y2⟩)= ?
Does f(⟨x1,y1⟩+⟨x2,y2⟩)=f(⟨x1,y1⟩)+f(⟨x2,y2⟩) for all ⟨x1,y1⟩,⟨x2,y2⟩∈ℝ^2?
b-
f(c⟨x,y⟩)=
c(f(⟨x,y⟩))=
Does f(c⟨x,y⟩)=c(f(⟨x,y⟩)) for all c∈ℝ and all ⟨x,y⟩∈ℝ2
c-Is f a linear transformation?
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