Find inverse matrix of A
1. 1. 1. 1. O. 0
8. 4. 1. X. =. 0. 1. 0
27. 9. 1. 0. 0. 1
. a b. c
X =. d. e. f
. g. h. i
Then
a + d + g = 1
b + e + h = 0
c + f + i = 0
8a + 4d + g = 0
8b + 4e + h = 1
8c + 4f + i = 0
27a + 9d + g = 0
27b + 9e + h = 0
27c + 9f + i = 1
THEN NOW reorganize and find a,d, g with
a + d + g = 1
8a + 4d + g = 0
27a + 9d + g = 0
THEN a= 5/22,. d = -19/22,. g= 18/11
NOW find b, e, h with
b + e + h = 0
8b + 4e + h = 1
27b + 9e + h = 0
As a result,. b = -4/11. e= 13/11,. h= -9/11
NOW FIND c, f, i. By means of
c + f + i = 0
8c + 4f + i= 0
27c + 9f + i = 1
Then is obtained, c = 3/22,. f = -7/22,. i= 2/11
SO THEN finally write Inverse matrix
5/22. -4/11. 3/22
-19/22. 13/11. -7/22
18/11. -9/11. 2/11
THEN NOW MULTIPLY this matrix by
. 116
. 448
. 972
THEN
a = (5/22)• 116 -(4/11)•448 +(3/22)•972 = 26.36 -162.9 + 132.54 = -4
b = (-19/22)•116 + (13/11)•448 - (7/22)•972= -100.2 + 529.45 -309.27 = 120
c= (18/11)•116 -(9/11)•448 + (2/11)•972 = 189.81 - 366.5454 + 176.7272= 0
THEREFORE THE EQUATION SEARCHED IS
Y = -4X^3 + 120X^2