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