Suppose that C AB with AB and C being matrices Problem 3 Ch

Suppose that C = AB, with A,B and C being matrices Problem 3 Choose the correct word from each pair of parentheses to complete the following sentences. (a) Column-j of AB is a linear combination of (columns or rows) of (A or B). (b) Row-i of AB is a linear combination of (columns or rows) of (A or B).

Solution

a. column j of AB is a linear combination of columns of B

b. Row i of AB is a linear combination of rows of A.

Reason for above answers:

Two matrices can be multiplied if and only if, the number of columns in the first matrix is equal to the number of rows in the second matrix. The order of the resultant matrix is (number of rows of first matrix) × (number of columns of second matrix).