Why does Matlab have a different solution than mine? I tried other software, and they give me the same solution.

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Matteo Geraci
Matteo Geraci 2020-7-16
评论： Matteo Geraci 2020-8-4
%matrix A, and vector of constants b
A = [2 1 0 0 0; 1 1 -1 0 -1; -1 0 1 0 1; 0 -1 0 1 1; 0 1 1 1 1]
b = [100; 0; 50; 120; 0]
%augmented matrix
Ab = [A b]
%row reduction
[rowreducedAb, pivotvarsAb] = rref(Ab)
%free and basic variables
[numqns, numvars] = size(A)
[numrows, numpivotvars] = size(pivotvarsAb)
numfreevars = numvars - numpivotvars
%LU decomposition of A
[L,U] = lu(A)
y = L\b
%inverse of U
invU = inv(U)
%original solution
x = invU*y
%cramer's rule
A1 = A
A1(:,1) = b
x1 = det(A1)/det(A)
My Solution:
Matrix A Vector of unknows Vector of constants
2 1 0 0 0 x1 100
1 1 -1 0 -1 x2 0
-1 0 1 0 1 x3 50
0 -1 0 1 1 x4 120
0 1 1 1 1 x5 0
Fourth Step: Gaussian Eliminations;
B + C -> B x2 = 50
A - B -> A x1 = 25
D + E -> D
D - C -> D
D) x1 + x5 = 70 x5 = 45
C) -x1 + x3 + x5 = 50 x3 = 25 - 45 + 50 x3 = 30
E) x2 + x3 - x4 + x5 = 0 50 + 30 + 45 = x4 x4 = 125

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采纳的回答

Walter Roberson
Walter Roberson 2020-7-16
Back substitute on your proposed solution
>> A*[25;50;30;125;45]
ans =
100
0
50
120
250
The first four entries match b, but the last entry of b is 0 not 250. Your solution is incorrect.
>> A\b
ans =
25
50
-220
-125
295
>> A*[25;50;-220;-125;295]
ans =
100
0
50
120
0
MATLAB's solution works.

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