Multiplying Matrices by Scalar
The product of a real number x, called a scalar, and a matrix M is a new matrix xM, where xM stands for the multiplication of all the elements of matrix M by scalar x.
Multiply the scalar 5 by the matrix .
Properties of Scalar Multiplication
Let M and N be x y matrices, and let m and n be scalars. The following are the properties of scalar multiplication:
- Associative Property(mn)(M) = m(nM)
- Distributive Property(m + n)M = mM + nM
- Distributive Propertym(M + N) = mM + mN
- Scalar Identity1M = M
- Associative Propertym(M)n = mn(M)