Question 896268: Consider the following system of linear equations.
2x + 3y + z = −1
3x + 3y + z = 1
2x + 4y + z = −2
(i). Write the system in the form Ax = b.
(ii). Find the inverse, A
, of A.
(iii). Use A−1
to find x.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 2x + 3y + z = −1
3x + 3y + z = 1
2x + 4y + z = −2
2,3,1,-1
3,3,1,1
2,4,1,-2
divide row 1 by 2
1,3/2,1/2,-1/2
3,3,1,1
2,4,1,-2
add down (-3) *row 1 to row 2
1,3/2,1/2,-1/2
0,-3/2,-1/2,5/2
2,4,1,-2
add down (-2) *row 1 to row 3
1,3/2,1/2,-1/2
0,-3/2,-1/2,5/2
0,1,0,-1
divide row 2 by -3/2
1,3/2,1/2,-1/2
0,1,-2/-6,10/-6
0,1,0,-1
add down (-1) *row 2 to row 3
1,3/2,1/2,-1/2
0,1,1/3,5/-3
0,0,-1/3,-2/-3
divide row 3 by -1/3
1,3/2,1/2,-1/2
0,1,1/3,5/-3
0,0,1,-2
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1/3) *row 3 to row 2
1,3/2,1/2,-1/2
0,1,0,-1
0,0,1,-2
add up (-1/2) *row 3 to row 1
1,6/4,0,2/4
0,1,0,-1
0,0,1,-2
add up (-3/2) *row 2 to row 1
1,0,0,2
0,1,0,-1
0,0,1,-2
final
1,0,0,2
0,1,0,-1
0,0,1,-2
1,0,0,2
0,1,0,-1
0,0,1,-2
"2","-1","-2"
(2,-1,-2)
determinant of
2,3,1
3,3,1
2,4,1
= 1
x = 2/1 = 2/1 = 2
y = -1/1 = -1/1 = -1
z = -2/1 = -2/1 = -2
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