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12 votes
Use coefficient matrix and the supplied data to find the coefficients a, b and c in the equation

User Priyanka Gupta
by
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1 Answer

21 votes
21 votes

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

User Harshil Pansare
by
2.9k points