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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.

Finding the inverse of a matrix is closely related to solving systems of linear equations: 1 3 a c 1 0 = 2 7 b d 0 1 A A−1 I can be read as saying ”A times column j of A−1 equals column j of the identity matrix”. This is just a special form of the equation Ax = b. Gauss-Jordan Elimination

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