Suppose f: R² → R² is a linear transformation. The two pictures on top in the figure use standard S-coordinates, where S = {e₁,e₂}. The two figures on bottom in the figure use B-coordinates, where B = {b₁,b₂}. The figure shows the vectors b₁ and b₂ in blue and the vectors f(b₁) and f(b₂) in red. Standard basis S= {e₁,e₂} y 4 3 2 1 -1 -2 -9 -4 -4-3-2-1 b1 b1 b2 [id] ↑ 19 1 2 3 b2 Custom basis B = {b₁,b₂} 4 X [f]'s [f] B →> 4 3 2 1 -1 -2 -9 -4 Standard basis S = {e₁,e₂} y -4-3-2-1 f(b2) पं b1 b2 19 1 2 [id] ↑ b1 b2 44 (b1) 3 4 Custom basis B= {b₁,b₂} X
Suppose f: R² → R² is a linear transformation. The two pictures on top in the figure use standard S-coordinates, where S = {e₁,e₂}. The two figures on bottom in the figure use B-coordinates, where B = {b₁,b₂}. The figure shows the vectors b₁ and b₂ in blue and the vectors f(b₁) and f(b₂) in red. Standard basis S= {e₁,e₂} y 4 3 2 1 -1 -2 -9 -4 -4-3-2-1 b1 b1 b2 [id] ↑ 19 1 2 3 b2 Custom basis B = {b₁,b₂} 4 X [f]'s [f] B →> 4 3 2 1 -1 -2 -9 -4 Standard basis S = {e₁,e₂} y -4-3-2-1 f(b2) पं b1 b2 19 1 2 [id] ↑ b1 b2 44 (b1) 3 4 Custom basis B= {b₁,b₂} X
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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