College Algebra Matrices
The Scalar Product Concepts 1

|  |  | Statement |  |
. |
The scalar product of a matrix and a real number to be the matrix with each entry equal to the product of that real number and the corresponding entry in the given matrix. If A=(aij)m x n and k is any real number, then the scalar product of A and k is kA = (k aij)m x n, that is

Example. Evaluate the product

Properties of the Scalar Product If A, B are matrices, k1, k2 are real numbers, then k1(A + B) = k1A + k1B, (k1+k2)A = k1A + k2A, k1(k2A) = (k1k2)A.

Copyright © 1998-2001 MathAid, LLC. All rights reserved.