2.3.1 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 

Leave a Comment