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If L : V → W is a linear transformation which of the following is FALSE? O None of these O If L is one-to-one, then ker L forms a basis for V. ○ If dim(V) = dim(W), then either L is both one-to-one and onto or L is neither one-to-one nor onto. ○ If L is onto, then every vector in W is an image of at least one vector in V.

If L : V → W is a linear transformation which of the following is FALSE? O None of these O If L is one-to-one, then ker L forms a basis for V. ○ If dim(V) = dim(W), then either L is both one-to-one and onto or L is neither one-to-one nor onto. ○ If L is onto, then every vector in W is an image of at least one vector in V.

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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34. Linear Transformation

If L: V → W is a linear transformation which of the following is FALSE? None of these O If L is one-to-one, then ker L forms a basis for V. ○ If dim(V) dim(W), then either L is both one-to-one and onto or L is neither one-to-one nor onto. O If I is onto, then every vector in W is an image of at least one vector in V. -
Transcribed Image Text:If L: V → W is a linear transformation which of the following is FALSE? None of these O If L is one-to-one, then ker L forms a basis for V. ○ If dim(V) dim(W), then either L is both one-to-one and onto or L is neither one-to-one nor onto. O If I is onto, then every vector in W is an image of at least one vector in V. -
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