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)
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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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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