Solving a system of linear equations with a few known variables
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Deepa Maheshvare
on 11 Dec 2018
Commented: AKASH BHOYAR
on 19 May 2022
I'm solving the following system of linear equations,
Ax = b, some of the x's are knowns.
For example,
A=
-12 12 0 0 0
0 -1 1 0 0
0 0 -0.5 0.5 0
0 0 0 -17 17
x = [x1 x2 x3 x4 x5]
b = [b1 0 0 0 b5]
When some of the variables are known, say x1 and x5 are known, the system can be reduced in terms of the known variables. However, when there are around 50 variables and 5 are known re-writing the matrix in terms of the known variables is difficult.
I would like ask for suggestions on alternate ways of solving these kind of linear systems in which the values of a few variables are known.
2 Comments
KSSV
on 11 Dec 2018
To solve b should be having a length equal to rows of A. Read about mldivide i,e \
Accepted Answer
Bruno Luong
on 11 Dec 2018
Edited: Bruno Luong
on 11 Dec 2018
Assuming known is the logical index == TRUE for indexes of x that are known
% known = ismember(1:5,[1 5]) % in your example
x(known) = XValueYouKnow;
x(~known) = A(:,~known) \ (b-A(:,known)*x(known))
1 Comment
More Answers (1)
madhan ravi
on 11 Dec 2018
Edited: madhan ravi
on 11 Dec 2018
See https://in.mathworks.com/matlabcentral/answers/297297-how-to-solve-a-system-of-equations-in-the-matlab?s_tid=answers_rc1-2_p2_MLT#answer_230057 for detailed discussion.
One way using solve():
syms x1 x2 x3 x4 x5 b1 b5
eqn=[ -12*x1+12*x2==b1;
-x2+x3==0;
-0.5*x3+0.5*x4==0;
-17*x4+17*x5==b5];
[x1,x2,x3,x4]=solve(eqn)
Second way using linsolve():
syms b1 b5
A=[ -12 12 0 0 0
0 -1 1 0 0
0 0 -0.5 0.5 0
0 0 0 -17 17];
b = [b1;0;0;b5];
[x,R]=linsolve(A,b)
Third way using mldivide():
syms b1 b5
A=[ -12 12 0 0 0
0 -1 1 0 0
0 0 -0.5 0.5 0
0 0 0 -17 17];
b = [b1;0;0;b5];
A\b % x5 has infinity number of solutions I guess
10 Comments
madhan ravi
on 11 Dec 2018
My suggestion was already stated https://in.mathworks.com/matlabcentral/answers/435087-solving-a-system-of-linear-equations-with-a-few-known-variables#comment_648869
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