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Linear Algebra

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Moderate

Linear Transformation - $f(1, 2)$

LINALG-JI4UCJ

Suppose that $f: R^2\rightarrow R^3$ is a linear transformation and that $f((2,3))=(1,0,1)$ and $f((-1,1))=(0,1,0)$.

What, if anything, can you say about $f(1,2)$?

Select ALL that apply.

A

$f((1,2))\neq (0,0,0)$

B

$f((1,2))=(0,0,1)$

C

$f((1,2)=\cfrac{1}{5}(3,1,3)$

D

$f((1,2))=f((1,0))+f((0,2))$

E

$f((1,2))=f((2,1))$

F

None of the above are true.