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Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra + B)=rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O if L is a linear transformation, then L(ra) = rL(a) for all a E V %3D and scalar r. O IfL is a linear transformation, then L(a +B)3 L(@) +L(B) for all a, 8 E V.

Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra + B)=rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O if L is a linear transformation, then L(ra) = rL(a) for all a E V %3D and scalar r. O IfL is a linear transformation, then L(a +B)3 L(@) +L(B) for all a, 8 E V.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra +B)3rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O If L is a linear transformation, then L(ra) =rL(a) for all a E V and scalar r. O IfL is a linear transformation, then L(a+B) = L(a) +L(B) for all a, 8E V.
Transcribed Image Text:Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra +B)3rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O If L is a linear transformation, then L(ra) =rL(a) for all a E V and scalar r. O IfL is a linear transformation, then L(a+B) = L(a) +L(B) for all a, 8E V.
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