Multiplying Matrices by Scalar


Matrix Multiplication 


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.

Example 

Multiply the scalar 5 by the matrix .

Solution
       




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:
  1. Associative Property(mn)(M) = m(nM)
  2. Distributive Property(+ n)M = mM + nM
  3. Distributive Propertym(MN) = mM + mN
  4. Scalar Identity1M = M
  5. Associative Propertym(M)n = mn(M)

Exercises

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Answer Key

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