L and M are linear mappings represented by matrices. L is a 3x3 matrix and M is a 2x3 matrix. Composition a) L o M is not defined because the number of columns of M does not equal the number of rows of L. Composition b) M o L is defined, with domain R^3 and codomain R^2.

1. Let L and M be linear mappings with matrices [L] = [ 1 2 5 ] [ 6 -8 -1] [ 3 4 3 ] and [M]= [ -2 4 8
] [ 7 0 -9 ] Determine which of the following compositions are defined. For those that are
defined, determine the domain and codomain. For those that are not defined, give a reason why.
a) L o M b) M o L
Solution
let the linear mappings be Lx,Mx,,where x is 3x1....hence (a)LoM (x)=L(Mx)=LM(x)....
L is of order 3x3..and M is of 2x3 order ..hence LM is not defined.[since no. of columns of M is
not equal to no.of rows of M],....................
(b)MoL(x)=M(Lx)=ML(x)....here ML is defined,,,and ML is 46 -4 10
-20 -22 8
................hence (a)is not defined but (b)is defined