In a finite element system, three displacements are known to satisfy the following system of linear equations:
5 7 2 =1
4 3 6 =4
5 3 5 =4
2007-02-10 02:36:07 · 2 answers · asked by ozi 1 in Science & Mathematics ➔ Mathematics
I will rewrite them from the matrix form to the full
5x + 7y + 2z = 1 (1)
4x + 3y + 6z = 4 (2)
5x + 3y + 5z = 4 (3)
(2) - (3) gives
-x +z = 0
x = z
Subst for z = x in (1) and (2) gives
7x + 7y = 1 (4)
10x + 3y = 4 (5)
3*(4) and 7*(5) gives
21x + 21y = 3 (6)
70x + 21y = 28 (7)
(7) - (6) gives
49x = 25
x = 25/49
z = 25/49
Subst for x, z in (3)
250/49 + 3y = 4
3y = -54/49
y = -18/49
Thus, the solution is
x=z=25/49, y=-18/49
2007-02-10 04:35:54 · answer #1 · answered by aepacino 2 · 1⤊ 0⤋
3 equations with 3 unknowns.
Subtract the 3rd frome the 2nd, results in x=z
2007-02-10 10:50:37 · answer #2 · answered by arbiter007 6 · 0⤊ 2⤋