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Let T:R3 → R3 be a linear transformation such that T(1,0,0) = (1,2,2), T(0,1,0)= (0,1,1) and T(0,0,1)= (-1,1, – 2). Answer the following questions using techniques and results taught in the course so far. (a) Find a formula for T. Justify your answer. (b) Does T maps R³ onto R° ? Justify your answer. (c) Can T be a one-to-one transformation? Justify your answer. (d) Give an example of a linear transformation T:R² → R² that is not onto R and not one to one.

Let T:R3 → R3 be a linear transformation such that T(1,0,0) = (1,2,2), T(0,1,0)= (0,1,1) and T(0,0,1)= (-1,1, – 2). Answer the following questions using techniques and results taught in the course so far. (a) Find a formula for T. Justify your answer. (b) Does T maps R³ onto R° ? Justify your answer. (c) Can T be a one-to-one transformation? Justify your answer. (d) Give an example of a linear transformation T:R² → R² that is not onto R and not one to one.

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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Let T:R3 → R3 be a linear transformation such that T(1,0,0) = (1,2,2), T(0,1,0)= (0,1,1) and T(0,0,1)= (-1,1, – 2). Answer the following questions using techniques and results taught in the course so far. (a) Find a formula for T. Justify your answer. (b) Does T maps R³ onto R ? Justify your answer. (c) Can T be a one-to-one transformation? Justify your answer. (d) Give an example of a linear transformation T:R²→ R² that is not onto R and not one to one.
Transcribed Image Text:Let T:R3 → R3 be a linear transformation such that T(1,0,0) = (1,2,2), T(0,1,0)= (0,1,1) and T(0,0,1)= (-1,1, – 2). Answer the following questions using techniques and results taught in the course so far. (a) Find a formula for T. Justify your answer. (b) Does T maps R³ onto R ? Justify your answer. (c) Can T be a one-to-one transformation? Justify your answer. (d) Give an example of a linear transformation T:R²→ R² that is not onto R and not one to one.
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