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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? = ○ If L is a linear transformation, then L(u + v) u, v € V. L(u) + L(v) for all O If L is a linear transformation, then L(ru) = rL(u) for all u € V and scalar 1. O If L is a linear transformation, then L(0v) = Ow, where Oy is the zero vector in V while Ow is the zero vector in W. Olf L(ru + v) = rL(u)+L(v) for all u, v EV and scalar , then I is a linear transformation.

Let L : V → W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? = ○ If L is a linear transformation, then L(u + v) u, v € V. L(u) + L(v) for all O If L is a linear transformation, then L(ru) = rL(u) for all u € V and scalar 1. O If L is a linear transformation, then L(0v) = Ow, where Oy is the zero vector in V while Ow is the zero vector in W. Olf L(ru + v) = rL(u)+L(v) for all u, v EV and scalar , then I is a linear transformation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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41. Vector Spaces

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 is a linear transformation, then L(u + v) = L(u) + L(v) for all u, v € V. transformation, then L(ru) = rL(u) for all u € Vand If I is a linear transformation, then L(0v) = Ow, where Oy is the zero vector in V while Ow is the zero vector in W. O If L is a linear scalar 1. ○ If L(ru + v) = rL(u) + L(v) for all u, v € Vand scalar sº, r, a linear transformation. then L is
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 is a linear transformation, then L(u + v) = L(u) + L(v) for all u, v € V. transformation, then L(ru) = rL(u) for all u € Vand If I is a linear transformation, then L(0v) = Ow, where Oy is the zero vector in V while Ow is the zero vector in W. O If L is a linear scalar 1. ○ If L(ru + v) = rL(u) + L(v) for all u, v € Vand scalar sº, r, a linear transformation. then L is
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