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Let T:R → R be define by T(x, y) = (x+2y,-3x+5y). a) Find the standard matrix for T.

Let T:R → R be define by T(x, y) = (x+2y,-3x+5y). a) Find the standard matrix for T.

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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**Problem 10** Let \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be defined by \[ T(x, y) = (x + 2y, -3x + 5y). \] a) Find the standard matrix for \( T \). b) Find the image of \( \mathbf{u} = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \) under \( T \), \( T(\mathbf{u}) \).
Transcribed Image Text:**Problem 10** Let \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) be defined by \[ T(x, y) = (x + 2y, -3x + 5y). \] a) Find the standard matrix for \( T \). b) Find the image of \( \mathbf{u} = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \) under \( T \), \( T(\mathbf{u}) \).
Expert Solution
Step 1

Given:

Calculus homework question answer, step 1, image 1

For (a),

Now, T(1, 0) = (1+2(0), -3(1)+5(0)) = (1, -3).

And T(0, 1) = (0+2(1), -3(0)+5(1)) = (2, 5).

Thus, the standard matrix for T is 12-35.

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