# 線形方程式

### メモ

MuPAD® Notebook は将来のリリースでは削除される予定です。代わりに MATLAB® ライブ スクリプトを使用してください。

MuPAD Notebook ファイルを MATLAB ライブ スクリプト ファイルに変換するには、`convertMuPADNotebook` を参照してください。MATLAB ライブ スクリプトは、多少の違いはありますが、MuPAD 機能の大半をサポートします。詳細は、MuPAD Notebook を MATLAB ライブ スクリプトに変換を参照してください。

 `det` Determinant of a matrix `norm` Compute the norm of a matrix, a vector, or a polynomial `linalg::cond` Condition number of a matrix `linalg::matlinsolve` Solving systems of linear equations `linalg::matlinsolveLU` Solving the linear system given by an LU decomposition `linalg::rank` Rank of a matrix `linalg::toeplitzSolve` Solve a linear Toeplitz system `linalg::vandermondeSolve` Solve a linear Vandermonde system `numeric::det` Determinant of a matrix `numeric::inverse` Inverse of a matrix `numeric::rank` Numerical estimate of the rank of a matrix

## 例および操作のヒント

Choose a Solver

The general solvers (`solve` for symbolic solutions and `numeric::solve` for numeric approximations) handle a wide variety of equations, inequalities, and systems. When you use the general solver, MuPAD identifies the equation or the system as one of the types listed in the table that follows. Then the system calls the appropriate solver for that type. If you know the type of the equation or system you want to solve, directly calling the special solver is more efficient. When you call special solvers, MuPAD skips trying other solvers. Direct calls to the special solvers can help you to:

Solve Algebraic Systems

When solving a linear system of symbolic equations, the general solver returns a set of solutions:

Invert Matrices

To find the inverse of a matrix, enter `1/A` or `A^(-1)`:

Compute Determinants and Traces of Square Matrices

MuPAD provides the functions for performing many special operations on matrices. You can compute the dimensions of a matrix, swap or delete columns and rows, or transpose a matrix. For square matrices, you can compute determinants and traces.

Compute Rank of a Matrix

The rank of a matrix is the number of independent rows of a matrix. For a matrix in its reduced row echelon form, the rank is the number of nonzero rows. To compute the rank of a matrix, use the `linalg::rank` function. For example, compute the rank of the following square matrix:

Compute Determinant Numerically

To compute the determinant of a square matrix numerically, use the `numeric::det` function. For example, compute the determinant of the 5 ×5 Pascal matrix:

## 概念

Linear Algebra Library

Use only in the MuPAD Notebook Interface. This functionality does not run in MATLAB.

Numeric Algorithms Library

Use only in the MuPAD Notebook Interface. This functionality does not run in MATLAB.

#### Mathematical Modeling with Symbolic Math Toolbox

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