Determine which of the following functions are linear transformations. For each function, either prove that it is a linear transformation of explain why it is not. (a) S: R² R² given by (b) T: P₂ → P₁ given by I s([*]) = [2+³+1] T(co+c₁x + c₂²) = −c₁ + ₂x. where co, C1, C₂ are constants. (c) F: M2,2 M2,2 given by F(A) = A-AT.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
Question
Determine which of the following functions are linear
transformations. For each function, either prove that it is a linear
transformation of explain why it is not.
(a) S: R² R² given by
(b) T: P₂ → P₁ given by
I
s([*]) = [2+³+1]
T(co+c₁x + c₂²) = −c₁ + ₂x.
where co, C1, C₂ are constants.
(c) F: M2,2 M2,2 given by
F(A) = A-AT.
Transcribed Image Text:Determine which of the following functions are linear transformations. For each function, either prove that it is a linear transformation of explain why it is not. (a) S: R² R² given by (b) T: P₂ → P₁ given by I s([*]) = [2+³+1] T(co+c₁x + c₂²) = −c₁ + ₂x. where co, C1, C₂ are constants. (c) F: M2,2 M2,2 given by F(A) = A-AT.
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