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4.5 Multiplication of Two Matrices (Sample Question 2)

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Example 2:
Find the values of m and n in each of the following matrix equations.
( a ) ( 3 m ) ( 1       n ) = ( 3 12 − 2 − 8 ) ( b ) ( m 2 − 3 1 ) ( 2 n ) = ( 12 4 + 2 n ) ( c ) ( m − 3 − 1 1 ) ( − 1 2 4 n ) = ( − 14 − 11 5 3 )
 
Solution:
(a) ( 3 m ) ( 1   n ) = ( 3 12 − 2 − 8 ) ( 3 3 n m m n ) = ( 3 12 − 2 − 8 ) m = − 2 ,   3 n = 12 n = 4

(b) ( m 2 − 3 1 ) ( 2 n ) = ( 12 4 + 2 n ) ( 2 m + 2 n − 6 + n ) = ( 12 4 + 2 n ) − 6 + n = 4 + 2 n n = − 10 2 m + 2 n = 12 2 m + 2 ( − 10 ) = 12 2 m − 20 = 12 2 m = 32 m = 16

(c) ( m − 3 − 1 1 ) ( − 1 2 4 n ) = ( − 14 − 11 5 3 ) ( − m + ( − 12 ) 2 m + ( − 3 n ) 1 + 4 − 2 + n ) = ( − 14 − 11 5 3 ) − m − 12 = − 14 − m = − 2 m = 2 − 2 + n = 3 n = 5