Let D, be the linear transformation from C'[a, b] into C[a, b] from this example. Determine whether the statement is true or false. Explain. 0₂ (+8 + 7x) = 0₁ (+8) + 70 x(x) O True, D, is a linear transformation and preserves addition and scalar multiplication. O False, Dx is a linear transformation and preserves scalar addition and multiplication. O True, D is a linear transformation and preserves scalar addition and multiplication. O False, D, is a linear transformation but does not preserve or produce non-linear transformations.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 32E
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Let Dy be the linear transformation from C'[a, b] into C[a, b] from this example. Determine whether the statement is true or false. Explain.
D(+8 + 7x) = 0₂ (²+8) + 70₂(x)
D
O True, D is a linear transformation and preserves addition and scalar multiplication.
O False, D, is a linear transformation and preserves scalar addition and multiplication.
True, Dx is a linear transformation and preserves scalar addition and multiplication.
O False, Dx is a linear transformation but does not preserve or produce non-linear transformations.
Transcribed Image Text:Let Dy be the linear transformation from C'[a, b] into C[a, b] from this example. Determine whether the statement is true or false. Explain. D(+8 + 7x) = 0₂ (²+8) + 70₂(x) D O True, D is a linear transformation and preserves addition and scalar multiplication. O False, D, is a linear transformation and preserves scalar addition and multiplication. True, Dx is a linear transformation and preserves scalar addition and multiplication. O False, Dx is a linear transformation but does not preserve or produce non-linear transformations.
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