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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 \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be defined by \[ T(x, y) = (x + 2y, -3x + 5y) \].
Transcribed Image Text:10. Let \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be defined by \[ T(x, y) = (x + 2y, -3x + 5y) \].
c) Is \( b = \begin{bmatrix} 2 \\ -3 \end{bmatrix} \) in the image of \( T \)? Why or why not? d) Is \( T \) one-to-one? Justify your answer.
Transcribed Image Text:c) Is \( b = \begin{bmatrix} 2 \\ -3 \end{bmatrix} \) in the image of \( T \)? Why or why not? 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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