4.3 Addition and Subtraction of Matrices

4.3 Addition and Subtraction of Matrices
 
(A) Determining whether addition or subtraction can be performed on two given matrices
1. Two matrices can be added or subtracted if both matrices have the same order.
2. The addition or subtraction of two matrices is performed by adding or subtracting the corresponding elements of the matrices.


Example 1:
State whether the following matrices can be added or subtracted. Give reason to your answer.
  (a)  ( 2 3 )  and  ( 1    8 ) (b)  ( 1 2 7 1 )  and  ( 10 0 3 1 )  

(c) (p   2   4) and (2   6   q)

Solution:
(a) Cannot because the matrices are not of the same order.
(b) Can because the matrices are of the same order.
(c) Can because the matrices are of the same order.



Example 2:
Express each of the following matrices as a single matrix.
If A = ( 3 2 ) and B = ( 5 1 ) , then (a) A + B = ( 3 2 ) + ( 5 1 ) = ( 3 + 5 2 + 1 ) = ( 8 3 )


( b ) B A = ( 3 2 ) ( 5 1 ) = ( 3 5 2 1 ) = ( 2 1 )



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