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10. Let T: R → R² be define by T(x, y) = (x+2y,-3x+5y).

10. Let T: R → R² be define by T(x, y) = (x+2y,-3x+5y).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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10. Let T:R → R² be define by T(x, y) = (x+2y,–3x+5y).
Transcribed Image Text:10. Let T:R → R² be define by T(x, y) = (x+2y,–3x+5y).
2 in the image of T? Why or why not? -3 c) Is b= d) Is T one – to – one? Justify your answer.
Transcribed Image Text:2 in the image of T? Why or why not? -3 c) Is b= d) Is T one – to – one? Justify your answer.
Expert Solution
Step 1

Recall:

  • Let T:ℝn→ℝm is said to be one to one if u and v are the vectors in ℝn and T(u)=T(v) then u=v.
  • Let T:ℝn→ℝm is said to be onto if for every b in ℝm we can find atleast one x in ℝn with T(x)=b.
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