Consider the basis S = [v;. V2. V3} for Rº, where v = (1, 1, 1), v2 = (1, 1, 0), and v3 = (1,0,0), and let T:R3 - R° be the linear operator for which T(v,) = (3, – 1, 6), T(v2) = (4, 0, 1), T(v3) = (- 1, 7, 1) Find a formula for T(x1. X2. X3), and use that formula to find T(3, 6, – 1). T(3, 6, – 1) = (

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the basis S = [v;. V2. V3} for Rº, where v = (1, 1, 1), v2 = (1, 1, 0), and v3 = (1,0,0), and let T:R3 - R° be the linear operator for
which
T(v,) = (3, – 1, 6), T(v2) = (4, 0, 1), T(v3) = (- 1, 7, 1)
Find a formula for T(x1. X2. X3), and use that formula to find T(3, 6, – 1).
T(3, 6, – 1) = (
Transcribed Image Text:Consider the basis S = [v;. V2. V3} for Rº, where v = (1, 1, 1), v2 = (1, 1, 0), and v3 = (1,0,0), and let T:R3 - R° be the linear operator for which T(v,) = (3, – 1, 6), T(v2) = (4, 0, 1), T(v3) = (- 1, 7, 1) Find a formula for T(x1. X2. X3), and use that formula to find T(3, 6, – 1). T(3, 6, – 1) = (
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