x = A\B solves
the system of linear equations A*x = B. The matrices A and B must
have the same number of rows. MATLAB® displays
a warning message if A is badly scaled or nearly
singular, but performs the calculation regardless.
If A is a scalar, A\B performs
element-wise division of A into B.
If A is a square n-by-n matrix
and B is a column vector with n elements
or a matrix with n rows, then x = A\B is
a solution to the equation A*x = B, if it exists.
If A is a rectangular m-by-n matrix
with m ~= n, and B is a column
vector with m elements or a matrix with m rows,
then A\B returns a least-squares
solution to the system of equations A*x= B.
x = mldivide(A,B) is
an alternative way to execute x=A\B, but is rarely used. It enables operator
overloading for classes.
Solve a linear system of equations involving
a singular matrix, C.
C = magic(4);
D = [34; 34; 34; 34];
x = C\D
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =
1.306145e-17.
x =
1.5000
2.5000
-0.5000
0.5000
MATLAB issues a warning but proceeds with the calculation. MATLAB might give a valid solution
even when working with a singular matrix. These solutions are often
not unique.
Solution, specified as a vector, full matrix, or sparse matrix.
If A is an m-by-n matrix
and B is an m-by-p matrix,
then x is an n-by-p matrix,
including the case when p==1.
x is sparse only if both A and B are
sparse matrices.
If A is a square matrix, A\B is
roughly equal to inv(A)*B, but MATLAB processes A\B differently
and more robustly.
If the rank of A is less than
the number of columns in A, then x = A\B is
not necessarily the minimum norm solution. The more computationally
expensive x = pinv(A)*B computes the minimum norm
least-squares solution.
For full singular inputs, you can compute the least-squares
solution using the function linsolve.
