# \(\text{Solve}\)¶

You can use the \(\text{Solve}\) function to find the matrix \(x\) given matrices \(A\) and \(y\) where \(A x = y\).

You can use the `\solve`

backslash command to insert this function.

The following variants of this function are available:

\(\text{matrix } \text{Solve} \left ( \text{<A>}, \text{<y>} \right )\)

The \(A\) and \(y\) matrices represent the terms to use to solve for matrix \(x\). Matrix \(y\) must be a column matrix with the same number of rows in \(A\). Matrix \(A\) must be a square matrix.

The function will return a column matrix containing one row for each column in \(A\).

To improve the accuracy of the solver, the \(\text{Solve}\) function will perform an equilibration on the matrix before performing LU factorization with row pivoting to find the solution. The equilibration operation is limited to powers of 2 so as to not reduce accuracy while lowering the condition number. To improve accuracy, the \(\text{Solve}\) will also use an iterative refinement algorithm to compute a solution.

Figure 203 shows the basic use of the \(\text{Solve}\) function.