Multivariable Math Question, Derivative Matrix

[wmhs]

Given two functions f and g. Let f: R5 to R3 and g: R3 to R4.
What are the dimensions of the derivative matrix of the composition g(f(x))?

a) 7x8
b) 5x4
c) 4x5
d) 8x7
e) the composition is undefined

Any guidance would be greatly appreciated! I'm torn between b or c, not sure which way would the correct set up.

 

[Deleted member 4993]

given two functions f and g. let f be R5 to R3 and g be R3 to R4. what are the dimensions of the derivative matrix?

a) 7x8
b) 5x4
c) 4x5
d) 8x7
e) the composition in undefined

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[wmhs]

i narrowed it to either b or c. my teacher explained it with an m and and n as the R^n and R^m but i got really lost.

I'm pretty sure the composition works so choice e is also out!

 

[Ishuda]

Given two functions f and g. Let f: R5 to R3 and g: R3 to R4.
What are the dimensions of the derivative matrix of the composition g(f(x))?

a) 7x8
b) 5x4
c) 4x5
d) 8x7
e) the composition is undefined

Any guidance would be greatly appreciated! I'm torn between b or c, not sure which way would the correct set up.

So what does f(x) look like:
\(\displaystyle f\begin{pmatrix}
x_1\\ x_2\\ x_3\\ x_4\\ x_5\end{pmatrix}\, =\, \mathbf{y}\, =\,
\begin{pmatrix}
y_1\\ y_2\\ y_3\end{pmatrix}\, =\,
\begin{pmatrix}
a_{1,1}& a_{1,2}& ... & a_{1,5}\\
a_{2,1}& a_{2,2}& ... & a_{2,5}\\
a_{3,1}& a_{3,2}& ... & a_{3,5}\\
\end{pmatrix}
\begin{pmatrix}
x_1\\ x_2\\ x_3\\ x_4\\ x_5\end{pmatrix}\)

So, what does g(f(x)) = g(\(\displaystyle \mathbf{y}\)) look like?