SOLUTION: without using cocept of inverse of a matrix , solve the following matrix equation: 5 4 x=1 -2 1 1 1 3 where x is a 2×2 matrix.

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Question 923156: without using cocept of inverse of a matrix , solve the following matrix equation:
5 4 x=1 -2
1 1 1 3
where x is a 2×2 matrix.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29
Then,

Looking at each element,
1.5a%2B4c=1
2.5b%2B4d=-2
3.a%2Bc=1
4.b%2Bd=3
From eq. 3,
a=1-c
From eq. 4,
b=3-d
Substitute in eq. 1 and 2,
5%281-c%29%2B4c=1
5-5c%2B4c=1
5-c=1
c=4
Then,
a=1-4=-3
.
.
5%283-d%29%2B4d=-2
15-5d%2B4d=-2
15-d=-2
-d=-17
d=17
Then,
b=3-17=-14
So then,
x=%28matrix%282%2C2%2C-3%2C-14%2C4%2C17%29%29