Adding and Subracting Matrices


Matrix Operations

A matrix is often used to represent a series of operations, but you can perform operations on matrices themselves. 


Addition and Subtraction

Addition and subtraction are rather straightforward with matrices, just add or subtract the corresponding elements.









Addition and subtraction can only be done if the matrices have the exact same order.  In other words, both the number of rows and the number of columns has to be the same on both matrices.

 cannot be done


Multiplication By Scalar

The product of a real number k, called a scalar, and a matrix M is a new matrix kM, where kM stands for the multiplication of all the elements of matrix M by scalar k.

Example 

Multiply the scalar 5 by the matrix .

Solution
       



Properties of Scalar Multiplication

Let M and N be matrices of the same order, 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  →  (m + n)M = mM + nM
  3. Distributive Property  →  m(M + N) = mM + mN
  4. Scalar Identity  →  1M = M
  5. Scalar Commutative Property  →  m(M)n = mn(M)



Exercises

Perform the following operations if possible.


1.)

2.)


3.)

 


4.)




5.)






























Answer Key

1.)

2.)  not possible


3.)


4.) 


5.)