let L,M,N be linear mappings with matrices
[L]=[ 1 4] [M]=[3 2 2 0] [N]=[ 2 1 1]
[ 3 2] [1 -1 -1 2] [ 3 1 4]
[-1 0] [-3 0 7]
[ 1 -4 1]
Determine which of the following compositions are defined and determine the domain and co-domain of those that are defined
a) L o M b) M o L c) L o N

Question

let L,M,N be linear mappings with matrices 
[L]=[ 1   4]  [M]=[3  2    2  0]   [N]=[  2   1  1]
       [ 3   2]          [1 -1 -1  2]           [  3   1  4]
       [-1  0]                                        [-3   0  7]
                                                          [  1 -4  1]
Determine which of the following compositions are defined and determine the domain and co-domain of those that are defined
a) L o M              b) M o L            c) L o N

anonymous · Answer

sorry there are only three matrices I swear those brackets were lined up when I wrote it

anonymous · Answer

also I used o instead of the symbol as I could not find it it just means L(M(x))

jim_thompson5910 · Answer

kinda odd notation, but I think L o M  means

LMx

where x is any vector in R4

jim_thompson5910 · Answer

Oh wait, i misread, the notation makes a bit more sense. L and M aren't matrices.

jim_thompson5910 · Answer

so all you have to do (I think) is determine which matrix products are defined and determine the domain and codomain

ex: LM is defined because the inner dimensions match

you're going from R4 to R3, so the domain is R4 and the codomain is R3

anonymous · Answer

Okay that was my first reaction but I ended up confusing myself with what exactly the matrices they gave me were thanks.

jim_thompson5910 · Answer

np