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QUESTION 1 Consider the basis S = {v1, v2, v3} for R³, where (2,3,5), v2 = (1,5,0),and v3 = (7,0,0). T:R³ → R² is a linear transformation such %3D that T(v,) = (4,7), T(v2) = (5,0) and T(v3) = (1,3). Find a formula for T(x1,x2,x3); then use this formula to compute T(1,1,1).

QUESTION 1 Consider the basis S = {v1, v2, v3} for R³, where (2,3,5), v2 = (1,5,0),and v3 = (7,0,0). T:R³ → R² is a linear transformation such %3D that T(v,) = (4,7), T(v2) = (5,0) and T(v3) = (1,3). Find a formula for T(x1,x2,x3); then use this formula to compute T(1,1,1).

Advanced Engineering Mathematics
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 1 Consider the basis S = {v1, V2, v3} for R³, where vi = (2,3,5), v2 = (1,5,0),and v3 (7,0,0). T:R³ → R² is a linear transformation such that T(v,) = (4,7), T(v2) = (5,0) and T(v3) = (1,3). %3D %3D Find a formula for T(x1,x2, X3); then use this formula to compute T(1,1,1).
Transcribed Image Text:QUESTION 1 Consider the basis S = {v1, V2, v3} for R³, where vi = (2,3,5), v2 = (1,5,0),and v3 (7,0,0). T:R³ → R² is a linear transformation such that T(v,) = (4,7), T(v2) = (5,0) and T(v3) = (1,3). %3D %3D Find a formula for T(x1,x2, X3); then use this formula to compute T(1,1,1).
QUESTION 2 Consider the basis S = {v1, v2, v3} for R³, where v1 = (2,2,2), v2 = (1,2,3),and v3 (0,1,0). T:R³ → R² is a linear transformation such that T(v,) = (2,1), T(v2) = (7,1) and T(v3) = (0,5). %3D Find a formula for T(x1,x2, X3); then use this formula to compute T(2,5,2).
Transcribed Image Text:QUESTION 2 Consider the basis S = {v1, v2, v3} for R³, where v1 = (2,2,2), v2 = (1,2,3),and v3 (0,1,0). T:R³ → R² is a linear transformation such that T(v,) = (2,1), T(v2) = (7,1) and T(v3) = (0,5). %3D Find a formula for T(x1,x2, X3); then use this formula to compute T(2,5,2).
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