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Problem 5 () (a)Given matrix S that O(A)S== O(B)S== O(C)S== cont. x'=2x-3y y' = x+y ¹ ( ₁ ) = $(*) ² S basis? (D)S=12) 23 0(E)S = (²2) 1 3 -1 2 1 1 cont. -1 2, 1 2 -1 2 1 O(A) (1) and (²) O(B) (¹) and (2) (1) and (2) (b) What are the basis vectors i and in the original + (D) (1) and (2) (E) () and (2) (c) If a point P' = (₂) co-ordinates in the original basis? O(E)S = O(A)S= O(B)S = (3) O(C)S= O(D)S= What is the transformation (3) in the new basis, what is its cont.. evalu O(A) O(B) O(C O(D O(E)

Problem 5 () (a)Given matrix S that O(A)S== O(B)S== O(C)S== cont. x'=2x-3y y' = x+y ¹ ( ₁ ) = $(*) ² S basis? (D)S=12) 23 0(E)S = (²2) 1 3 -1 2 1 1 cont. -1 2, 1 2 -1 2 1 O(A) (1) and (²) O(B) (¹) and (2) (1) and (2) (b) What are the basis vectors i and in the original + (D) (1) and (2) (E) () and (2) (c) If a point P' = (₂) co-ordinates in the original basis? O(E)S = O(A)S= O(B)S = (3) O(C)S= O(D)S= What is the transformation (3) in the new basis, what is its cont.. evalu O(A) O(B) O(C O(D O(E)

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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Problem 5 () (a) Given matrix S that O(A)S == x' = 2x - 3y y' = x + y ¹ ( ₁ ) = $(*) ² S cont. O(B)S=; 1 2 O(C)S = ( -1 2 O(D)S = (12) O(E)S=231 -1 basis? O(A) (1) 1 O(B) cont. 1 3 -1 2 1 1 (b) What are the basis vectors i' and ' in the original -1 1 and (²) ¹ (²3) and O(C) -1 and OD) (1) a OCE) (1) and (2) and (c) If a point P' = - (₂) co-ordinates in the original basis? . What is the transformation O(A)S== O(B)S = (3) O(C)S= O(D)S== (3) O(E)S = (¹) in the new basis, what is its cont. (2²) evaluate the matrix in the new basis. (d) A matrix M = O(A)M' = O(B)M' = O(C)M' = O(D)M' = O(E)M' = 5 0 0 10 10 0 0 6 (7 0 0 10/ 5 10 0 0 10 0 07 in the original basis,
Transcribed Image Text:Problem 5 () (a) Given matrix S that O(A)S == x' = 2x - 3y y' = x + y ¹ ( ₁ ) = $(*) ² S cont. O(B)S=; 1 2 O(C)S = ( -1 2 O(D)S = (12) O(E)S=231 -1 basis? O(A) (1) 1 O(B) cont. 1 3 -1 2 1 1 (b) What are the basis vectors i' and ' in the original -1 1 and (²) ¹ (²3) and O(C) -1 and OD) (1) a OCE) (1) and (2) and (c) If a point P' = - (₂) co-ordinates in the original basis? . What is the transformation O(A)S== O(B)S = (3) O(C)S= O(D)S== (3) O(E)S = (¹) in the new basis, what is its cont. (2²) evaluate the matrix in the new basis. (d) A matrix M = O(A)M' = O(B)M' = O(C)M' = O(D)M' = O(E)M' = 5 0 0 10 10 0 0 6 (7 0 0 10/ 5 10 0 0 10 0 07 in the original basis,
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