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 )

Answer:
(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 )

Answer:
(a) ( 9 6 )( 7 2 )=( 97 6( 2 ) )=( 2 8 ) (b) ( 3 4 0 5 )( 7 3 6 1 ) =( 3( 7 ) 4( 3 ) 0( 6 ) 51 ) =( 3+7 4+3 0+6 51 )=( 10 1 6 4 )


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

Answer:
( p q )+( 5p 9 )=( 12 3q+1 ) ( p+5p q+9 )=( 12 3q+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 )

Answer:
( 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