We have the following linear map:
e is the standar basis of R^2 and
a is the standar basis of R^3
Question: Is there a linear map g: R^3-->R^2 that the matrix of (fog, a,a) is the 0 matrix?
Is there a linear map g: R^3-->R^2 that the matrix of (gof, e,e) is the 0 matrix?
The Attempt at a Solution
First of all the matrix of f for the standar basis is:
Α= 3 8
I also know that in general the matrix of a fog (i dont know the word maybe junction or merge?) is the matrix of f multiplied with the matrix of g.
Now, what i cant understand is how am I going to find what the matrix of fog or gof will look like, because f and g come from different dimension spaces. In other words if F is R^2-->R^3 and G is R^3-->R2 then what is FoG or GoF going to be? I prefer to get an answer to this rather than the actual homework question! Thanks in advance!
P.S again sorry for bad english its quite hard for me to find all those weird terms.