2. Consider the mappings L . M, N , and P given in the previous question . For each of the following compositions ." - Determine if it is defined ( meaning , check if the codomain of the mapping on the right is the domain of the mapping on the left , so that the composition is defined ) . If it is defined : - State its domain and codomain . - Determine if the mapping is linear : if it is prove this , otherwise explain why it is not linear . - If the mapping is linear find its standard matrix . ( 2 ) LOL ( b) NOL ( C ) POM ( d ) NOM1 . For each of the following mappings :" - State its domain and codomain ( meaning , each of these mappings is a function from some !`" to some* other HIM ; identify these " and m ) . - Determine if the mapping is linear ; if it is prove this , otherwise explain why it is not linear . - If the mapping is linear find its standard matrix [ recall , this is the matrix whose corresponding matrix mapping is equal to the original mapping ) . * 1 \\ = 2X'1 ( b ) M/ EX \\ * 1 + ^2 +*^` `/ 1 -^ O * 1 + 1'2\\ O U ( d ) P * 1 = | * 1 - 1 O