“augmented matrix”的概念、定义、翻译、参考文献-科学参考

augmented matrix

Mathematics

单词	augmented matrix
释义	augmented matrix Mathematics For a given set of m linear equations in n unknowns x₁, x₂,…x_n, $\begin{matrix} a_{11} x_{1} + a_{12} x_{2} + \dots + a_{1 n} x_{n} = b_{1}, \\ a_{21} x_{1} + a_{22} x_{2} + \dots + a_{2 n} x_{n} = b_{2}, \\ ⋮ \\ a_{m 1} x_{1} + a_{m 2} x_{2} + \dots + a_{m n} x_{n} = b_{m}, \end{matrix}$ the augmented matrix is the matrix $[\begin{matrix} a_{11} & a_{12} & \dots & a_{1 n} & b_{1} \\ a_{21} & a_{22} & \dots & a_{2 n} & b_{2} \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ \\ a_{m 1} & a_{m 2} & \dots & a_{m n} & b_{m} \end{matrix}]$ obtained by adjoining to the matrix of coefficients an extra column of entries taken from the right-hand sides of the equations. The solutions of a set of linear equations may be investigated by transforming the augmented matrix to echelon form or reduced echelon form by elementary row operations. See Gaussian elimination, Gauss-Jordan elimination.
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