Note that we have this matrix equation :
Ax = b where A = [5 -2 and b = [ 2
2 -1] -4]
If I multiply both sides of the equation [on the left] by the inverse of A, we have
(A-1) (A )x =( A-1 ) b
But (A-1) (A) is just the Identity matrix, I
So.....the left side just simplifies to x .......and we have
x = A-1 b
So.....we just need to find the inverse of A = A-1
Note, for a 2 x 2 matrix in the form of [ a b
c d ]
The inverse is given by : [1/ (ad - bc)] * [ d - b =
- c a]
[1 / (-5 +4)] * [ -1 2 = [-1] [ -1 2
-2 5] -2 5]
So.....the inverse of A = [1 - 2
2 -5]
So......
x = A-1 * b = [ 1 - 2 * [2 =
2 -5 ] -4]
[1*2 + -2*-4 = [ 2 +8 = [10
2*2 + - 5* -4 ] 4 +20] 24]
So....the last matrix is the answer.......
And that's it !!!!
