Addition and Subtraction on Matrices (Sample Questions)


Example 1:
Find the addition of the following matrices.
( a )   ( 18    7 ) + ( 3        6 ) ( b )   ( 13 0 7 1 ) + ( 1 3 5 6 )

Solution:
( a )   ( 18    7 ) + ( 3       6 ) = ( 18 + 3    7 + 6 ) = ( 21   1 ) ( b )   ( 13 0 7 1 ) + ( 1 3 5 6 ) = ( 13 + ( 1 ) 0 + 3 7 + 5 1 + 6 ) = ( 14 3 12 5 )



Example 2:

Find the subtraction of the following matrices.
( a ) ( 9 6 ) ( 7 2 ) ( b ) ( 3 4 0 5 ) ( 7 3 6 1 )

Solution:
( a ) ( 9 6 ) ( 7 2 ) = ( 9 7 6 ( 2 ) ) = ( 2 8 ) ( b ) ( 3 4 0 5 ) ( 7 3 6 1 ) = ( 3 ( 7 ) 4 ( 3 ) 0 ( 6 ) 5 1 ) = ( 3 + 7 4 + 3 0 + 6 5 1 ) = ( 10 1 6 4 )


Example 3:

Given that ( p q ) + ( 5 p 9 ) = ( 12 3 q + 1 )  , find the values of p and q.

Solution:

( p q ) + ( 5 p 9 ) = ( 12 3 q + 1 ) ( p + 5 p q + 9 ) = ( 12 3 q + 1 )
 
p + 5p = 12
6p = 12
p = 2
q + 9 = 3q + 1
q – 3q = 1 – 9
2q = 8
q = 4


Example 4:
Find the values of m and n in the following matrix equation.
( 7 6 n 1 ) ( 1 m 4 2 ) = ( 5 12 6 11 )

Solution:
( 7 6 n 1 ) ( 1 m 4 2 ) = ( 5 12 6 11 )

6 – m = 12
 –m = 6
 m = –6
n – (–4) = 6
n + 4 = 6
n = 2 

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