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Linear Algebra

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Moderate

Showing Linearity

LINALG-VDIKJW

Suppose that $V,W$ are vector spaces and $f:V\rightarrow W$ is a function.

What do you need to do to show that $f$ is a linear transformation?

A

Nothing, all functions from $V$ to $W$ are linear transformations.

B

You must show that $f(x+y)=f(x)+f(y)$ for all $x,y\in V$.

C

You must show that $f(rx)=rf(x)$ for all real numbers $r$ and all $x\in V$.

D

You must show that $f(xy)=f(x)f(y)$ for all $x,y\in V$.

E

You need to show both Choices 'B' and 'C'.

F

You need to show both Choices 'B' and 'D'.

G

You need to show Choices 'B', 'C' and 'D'.