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3b) Change of Basis--Finding the transition matrix: 3c). i) Find a matrix that will rename points from the blue coordinate system as points in the black one. Call this matrix P. ii) How are the columns of P related to the basis vectors of the blue coordinate system? iii) Find a matrix that will rename points from the black coordinate system as points in the blue one. iv) How is this matrix related to the P matrix? Recall the linear transformation from Task 1: vectors along the line y = -3x get stretched by a factor of 2, and vectors along the line y = x remain fixed. Determine what happens to each of the vectors below under the transformation. Express the result in both the blue and the black coordinate systems. Describe your methods both graphically and with matrix equations. 1. [x1]blue = [] 2. [x2]bine = [3] 3. [x3]black- 3) The Blue and Black Task Consider the following two coordinate systems of R2: the black coordinate system and the blue coordinate system. b d C a e 3a). Write the coordinates of each of the above points relative to both the blue and the black coordinate systems.

3b) Change of Basis--Finding the transition matrix: 3c). i) Find a matrix that will rename points from the blue coordinate system as points in the black one. Call this matrix P. ii) How are the columns of P related to the basis vectors of the blue coordinate system? iii) Find a matrix that will rename points from the black coordinate system as points in the blue one. iv) How is this matrix related to the P matrix? Recall the linear transformation from Task 1: vectors along the line y = -3x get stretched by a factor of 2, and vectors along the line y = x remain fixed. Determine what happens to each of the vectors below under the transformation. Express the result in both the blue and the black coordinate systems. Describe your methods both graphically and with matrix equations. 1. [x1]blue = [] 2. [x2]bine = [3] 3. [x3]black- 3) The Blue and Black Task Consider the following two coordinate systems of R2: the black coordinate system and the blue coordinate system. b d C a e 3a). Write the coordinates of each of the above points relative to both the blue and the black coordinate systems.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3b) Change of Basis--Finding the transition matrix: 3c). i) Find a matrix that will rename points from the blue coordinate system as points in the black one. Call this matrix P. ii) How are the columns of P related to the basis vectors of the blue coordinate system? iii) Find a matrix that will rename points from the black coordinate system as points in the blue one. iv) How is this matrix related to the P matrix? Recall the linear transformation from Task 1: vectors along the line y = -3x get stretched by a factor of 2, and vectors along the line y = x remain fixed. Determine what happens to each of the vectors below under the transformation. Express the result in both the blue and the black coordinate systems. Describe your methods both graphically and with matrix equations. 1. [x1]blue = [] 2. [x2]bine = [3] 3. [x3]black-
Transcribed Image Text:3b) Change of Basis--Finding the transition matrix: 3c). i) Find a matrix that will rename points from the blue coordinate system as points in the black one. Call this matrix P. ii) How are the columns of P related to the basis vectors of the blue coordinate system? iii) Find a matrix that will rename points from the black coordinate system as points in the blue one. iv) How is this matrix related to the P matrix? Recall the linear transformation from Task 1: vectors along the line y = -3x get stretched by a factor of 2, and vectors along the line y = x remain fixed. Determine what happens to each of the vectors below under the transformation. Express the result in both the blue and the black coordinate systems. Describe your methods both graphically and with matrix equations. 1. [x1]blue = [] 2. [x2]bine = [3] 3. [x3]black-
3) The Blue and Black Task Consider the following two coordinate systems of R2: the black coordinate system and the blue coordinate system. b d C a e 3a). Write the coordinates of each of the above points relative to both the blue and the black coordinate systems.
Transcribed Image Text:3) The Blue and Black Task Consider the following two coordinate systems of R2: the black coordinate system and the blue coordinate system. b d C a e 3a). Write the coordinates of each of the above points relative to both the blue and the black coordinate systems.
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