Multiplying Matrices by Scalar

**Matrix Multiplication**

By Scalar

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:- Associative Property(
*mn*)(*M*) =*m*(*nM*) - Distributive Property(
*m*+*n*)*M*=*mM*+*nM* - Distributive Property
*m*(*M*+*N*) =*mM*+*mN* - Scalar Identity1
*M*=*M* - Associative Property
*m*(*M*)*n*=*mn*(*M*)

**Exercises**

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**Answer Key**

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