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.


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