Let ej denote the jth unit column that contains a 1 in the jth
position and zeros everywhere else. For a general matrix An×n, describe the following products. (a) Aej (c) eTiAej?
Rows and Columns of a Product
Suppose that A = [aij] is m × p and B = [bij] is p × n.
• [AB]i∗ = Ai∗B [( ith row of AB)=( ith row of A) ×B]. (3.5.4)
• [AB]∗j = AB∗j [ (jth col of AB)=A× ( jth col of B)]. (3.5.5)
• [AB]i∗ = ai1B1∗ + ai2B2∗ + · · · +aipBp∗ =Ʃ aikBk∗. (3.5.6)
• [AB]∗j = A∗1b1j + A∗2b2j + · · · + A∗pbpj=Ʃ A∗kbkj (3.5.7)
These last two equations show that rows of AB are combinations of
rows of B, while columns of AB are combinations of columns of A.
For parts a and c im not even sure what they are even asking for. When its saying ej is a unit column does that mean like this (1 0 0...0) as an example?