Give an example of a linear transformation

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SUMMARY

The discussion focuses on providing an example of a linear transformation in ℝ³ with a kernel spanned by the vector (-1, 1, 2). A proposed matrix was evaluated, revealing that it does not satisfy the kernel condition since the product Av does not yield the zero vector. The importance of understanding the definition of "kernel" in linear algebra is emphasized, along with the need to ensure matrix entries are correct to validate the transformation.

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Tonyt88
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Homework Statement


Give an example of a linear transformation whose kernel is the line spanned by:

-1
1
2

in lR³

Homework Equations





The Attempt at a Solution



Would:

1..(-1)...0
0...0...0
0..(-2)...1

be a solution?
 
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To prove it, prove your vector is in the kernel and that the dimension of the col. space is 3 - nullity = 2.
 
It quite obviously isn't since Av is not 0. Are you clear on the definition of "kernel"?

Actually your matrix has only a single entry wrong so it may be just a typo.
 

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