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karnten07
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[SOLVED] Linear transformations
Determine whether the following maps are linear transformations. (proofs or counterexamples required)
a.) L: R^2[tex]\rightarrow[/tex]R^2,
(x1)
(x2)
[tex]\mapsto[/tex]
(2x1 + 3x2)
(0)
The brackets should be two large brackets surrounding the two vectors.
I've been reading about linear transformations and i know i have to show something like:
L(x1+x2)= L(x1) +L(x2) and L(cx1)= cL(x1) where c is a scalar.
Is this right and i should treat x1 and x2 separately rather than the vector including x1 and x2 as one element of R^2?
What I am trying to say is, do i need to define a vector (y1, y2) as well in the set of R^2?
Homework Statement
Determine whether the following maps are linear transformations. (proofs or counterexamples required)
a.) L: R^2[tex]\rightarrow[/tex]R^2,
(x1)
(x2)
[tex]\mapsto[/tex]
(2x1 + 3x2)
(0)
The brackets should be two large brackets surrounding the two vectors.
The Attempt at a Solution
I've been reading about linear transformations and i know i have to show something like:
L(x1+x2)= L(x1) +L(x2) and L(cx1)= cL(x1) where c is a scalar.
Is this right and i should treat x1 and x2 separately rather than the vector including x1 and x2 as one element of R^2?
What I am trying to say is, do i need to define a vector (y1, y2) as well in the set of R^2?
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