Consider the basis S = {V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the linear operator for which - T(v₁)-(1, -2) and T(v₂) - (-4,1) Find a formula for T(x₁, x₂), and use that formula to find T(5,-3). i i T(5,-3) - (

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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Consider the basis S = {V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the linear operator for which
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T(v₁)-(1, -2) and T(v₂) - (-4,1)
Find a formula for T(x₁, x₂), and use that formula to find T(5,-3).
i
i
T(5,-3) - (
Transcribed Image Text:Consider the basis S = {V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the linear operator for which - T(v₁)-(1, -2) and T(v₂) - (-4,1) Find a formula for T(x₁, x₂), and use that formula to find T(5,-3). i i T(5,-3) - (
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