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Multiplication and Inverse Matrices - MIT OpenCourseWare

Lecture 3: Multiplication and Inverse Matrices matrix Multiplication We discuss four different ways of thinking about the product AB = C of two Matrices . If A is an m n matrix and B is an n p matrix , then C is an m p matrix . We use cij to denote the entry in row i and column j of matrix C. Standard (row times column). The standard way of describing a matrix product is to say that cij equals the dot product of row i of matrix A and column j of matrix B. In other words, n cij = aik bkj . k =1. Columns The product of matrix A and column j of matrix B equals column j of matrix C. This tells us that the columns of C are combinations of columns of A.

Matrix Multiplication We discuss four different ways of thinking about the product AB = C of two matrices. If A is an m × n matrix and B is an n × p matrix, then C is an m × p matrix. We use cij to denote the entry in row i and column j of matrix C. Standard (row times column)

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