Let v = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, v2, V3} is a basis for R³. Also, let T: R³ → R² be the linear map for which T(v1) = (1,0), T(v2) = (-1,1),T(v3) = (0,1). Then find T(7,13,7).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Let v, = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, v2, v3}
{V1, V2,
is a basis for R³. Also, let T: R³ → R² be the linear map for which
T(v1) = (1,0),T(v2) = (-1,1),T(v3) = (0,1). Then find T(7,13,7).
Transcribed Image Text:2. Let v, = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, v2, v3} {V1, V2, is a basis for R³. Also, let T: R³ → R² be the linear map for which T(v1) = (1,0),T(v2) = (-1,1),T(v3) = (0,1). Then find T(7,13,7).
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