Multilinear Functions I have a question regarding the properties of a multilinear function. This is for a linear algebra class. I know that for a multilinear function,
$f(cv_1,v_2,\dots,v_n)=c⋅f(v_1,v_2,\dots,v_n)$
Does this imply
$f(cv_1,dv_2,\dot,v_n)=c⋅d⋅f(v_1,v_2,\dots,v_n)$?
It is for a question involving a multilinear function $f:\mathbb{R}^2\times\mathbb{R}^2\times\mathbb{R}^2\to \mathbb{R}$. I am given eight values of $f$, each of which is composed of a combination three unit vectors. They are:
$f((1,0),(1,0),(1,0))=e$  
$f((1,0),(1,0),(0,1))=\sqrt{7}$
$f((1,0),(0,1),(1,0))=0$
$f((1,0),(0,1),(0,1))=2$
$f((0,1),(1,0),(1,0))=\sqrt{5}$ 
$f((0,1),(1,0),(0,1))=0 $
$f((0,1),(0,1),(1,0))=\pi$  
$f((0,1),(0,1),(0,1))=3$
Then I am asked to compute for different values of f. For instance,
$f((2,3),(-1,1),(7,4))$
How do I approach this question to solve for the value of $f$?

If I interpret your question correctly, then the clue is in $f:\mathbb{R}^2\times\mathbb{R}^2\times\mathbb{R}^2\to\mathbb{R}$, which seems to imply that the function is trilinear, that is, in three inputs of two dimensions each. In that case,
$\begin{align*}f((2,3),(-1,1),(7,4))
  =&2\cdot -1\cdot 7\cdot f((1,0),(1,0),(1,0))
\\+&2\cdot -1\cdot 4\cdot f((1,0),(1,0),(0,1))
\\+&2\cdot 1\cdot 7\cdot f((1,0),(0,1),(1,0))
\\+&2\cdot 1\cdot 4\cdot f((1,0),(0,1),(0,1))
\\+&3\cdot -1\cdot 7\cdot f((0,1),(1,0),(1,0))
\\+&3\cdot -1\cdot 4\cdot f((0,1),(1,0),(0,1))
\\+&3\cdot 1\cdot 7\cdot f((0,1),(0,1),(1,0))
\\+&3\cdot 1\cdot 4\cdot f((0,1),(0,1),(0,1))
\end{align*}$
I'll leave you to plug in the values, I'm too lazy. 
This might be easier to see if you realize that a bilinear function $f(x,y)=x'Ay$ (where $A$ is a matrix) works the same way.
