4.5 Multiplication of Two Matrices (Sample Question 2)


Example 2:
Find the values of m and n in each of the following matrix equations.
(a)(3m)(1     n)=(31228)(b)(m231)(2n)=(124+2n)(c)(m311)(124n)=(141153)
 
Solution:
(a)(3m)(1 n)=(31228)(33nmmn)=(31228)m=2, 3n=12n=4

(b)(m231)(2n)=(124+2n)(2m+2n6+n)=(124+2n)6+n=4+2nn=102m+2n=122m+2(10)=122m20=122m=32m=16

(c)(m311)(124n)=(141153)(m+(12)2m+(3n)1+42+n)=(141153)m12=14m=2m=22+n=3n=5