The solutions 𝒙 and 𝒚 of the linear systems 𝐴𝒙 = 𝒃1 and 𝐶𝒚 = 𝒃2

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

[Torsten]

help \

 \   Backslash or left matrix divide.
    A\B is the matrix division of A into B, which is roughly the
    same as INV(A)*B , except it is computed in a different way.
    If A is an N-by-N matrix and B is a column vector with N
    components, or a matrix with several such columns, then
    X = A\B is the solution to the equation A*X = B. A warning 
    message is printed if A is badly scaled or nearly singular.
    A\EYE(SIZE(A)) produces the inverse of A.
 
    If A is an M-by-N rectangular matrix with M~=N and B is a column
    vector with M components, or a matrix with several such columns,
    then X = A\B is the solution in the least squares sense to the
    under- or overdetermined system of equations A*X = B. The
    effective rank, K, of A is determined from the QR decomposition
    with pivoting. A solution X is computed which has at most K
    nonzero components per column. If K < N this will usually not
    be the same solution as PINV(A)*B.  A\EYE(SIZE(A)) produces a
    generalized inverse of A.
 
    X = MLDIVIDE(A,B) is called for the syntax 'A \ B' when A or B is an object.
 
    See MATLAB Operators and Special Characters for more details.
 
    See also LDIVIDE, RDIVIDE, MRDIVIDE, PAGEMLDIVIDE.

    Documentation for mldivide
       doc mldivide

    Other uses of mldivide

       codistributed/mldivide    laurpoly/mldivide
       comm/mldivide             StaticModel/mldivide
       distributed/mldivide      symbolic/mldivide
       duration/mldivide         tall/mldivide
       DynamicSystem/mldivide    timeseries/mldivide
       gpuArray/mldivide         tsdata.datametadata/mldivide
       LagOp/mldivide

Answer 1

[SAI SRUJAN]

Hi Aljohara,

I understand that you are facing an issue with finding the solution of a linear system of equations.

In MATLAB, solving linear systems of equations like 'Ax = b' can be done using the backslash operator('\').

Please follow the below code sample to proceed further,

% Define matrices
A = [1, 2; 3, 4];
b1 = [5; 6];
% Solve for x
x = A\b1;

For a comprehensive understanding of the '\' operator in MATLAB, please refer to the following documentation.

https://www.mathworks.com/help/matlab/ref/mldivide.html

I hope this helps!