Question

Solve the matrix equation for a, b, c, and d.

Answer 1

a+2c b+2d = 6 3
3a+4c 3b+4d 19 2

a+2c=6
a=6-2c

3a+4c = 19
3(6-2c)+4c = 19
18-6c+4c = 19
4c-6c = 19-18
-2c=1
c = -1/2

a = 6 - 2c
a = 6 - 2(-1/2)
a = 6+1
a=7

b+2d=3
b=3-2d

3b+4d=2
3(3-2d) + 4d = 2
9-6d +4d = 2
4d-6d = 2-9
-2d = -7
d = 7/2

b = 3-2d
b = 3-2(7/2)
= 3-7
= -4

a b = 7 -4
c d -1/2 7/2