Question

Let A be an m × k matrix and B be a k × n matrix. The product of A and B, denoted by AB, is the m × n matrix with its (i, j)th entry equal to the sum of the products of the corresponding elements from the ith row of A and the jth column of B.

true or false

Answer 1

The statement is true. The product of a matrix A with dimensions m x k and a matrix B with dimensions k x n is a new matrix AB with dimensions m x n.

Step-by-step explanation:

The statement is true. The product of a matrix A with dimensions m x k and a matrix B with dimensions k x n is a new matrix AB with dimensions m x n. To calculate the (i, j)th entry of the product matrix AB, we need to multiply the elements of the ith row of matrix A with the corresponding elements of the jth column of matrix B and then sum them up.