a. Does a3 =a₁ + a2? choose Does f(as) = f(a) + f(az)? choose b. Answer the following questions to determine whether / is a linear transformation. Entem ▪ f(a₁ +a₂) • f(a₁) + f(a₂) = 0.0 +

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 29E
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Question
Suppose f: R¹ R2 is a function and f(an) = b, for n = 1, 2, 3.
4
3
2
1
■
-1
-2
-3
-4
-4 -3 -2 -1
y
82
R
at
Domain
a3
1 2 3 4
X
ST
4
3
o -
2
-2
-3
he
-4-3-2-1
y
b1
1 2 3 4
Codomain
a. Does as = a₁ + a2? choose
Does f(a3) = f(a) + f(az)? choose
b. Answer the following questions to determine whether f is a linear transformation. Enter your answers as coordinate vectors of the form <1,2>:
f(a₁ +a₂) =
• ƒ(a₁) + f(a₂) = 0+
The function / choose
X
✓. Be sure you can explain your answer.
Transcribed Image Text:Suppose f: R¹ R2 is a function and f(an) = b, for n = 1, 2, 3. 4 3 2 1 ■ -1 -2 -3 -4 -4 -3 -2 -1 y 82 R at Domain a3 1 2 3 4 X ST 4 3 o - 2 -2 -3 he -4-3-2-1 y b1 1 2 3 4 Codomain a. Does as = a₁ + a2? choose Does f(a3) = f(a) + f(az)? choose b. Answer the following questions to determine whether f is a linear transformation. Enter your answers as coordinate vectors of the form <1,2>: f(a₁ +a₂) = • ƒ(a₁) + f(a₂) = 0+ The function / choose X ✓. Be sure you can explain your answer.
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