“reduced echelon form”的概念、定义、翻译、参考文献-科学参考

reduced echelon form

Mathematics

A matrix is in reduced echelon form if it is in echelon form and, further, every column that contains a leading 1 (of some row) otherwise has entries of 0. For example, these two matrices are in reduced echelon form:

$[\begin{matrix} 1 & 6 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & - 3 \\ 0 & 0 & 0 & 1 & 5 \end{matrix}], [\begin{matrix} 0 & 0 & - 1 & 4 & 2 \\ 0 & 1 & 2 & - 3 & 5 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}] .$

Any matrix can be transformed to a unique matrix in reduced echelon form using elementary row operations, by Gauss–Jordan elimination. The solutions of a system of linear equations can be immediately obtained from the reduced echelon form to which the augmented matrix has been transformed.

单词	reduced echelon form
释义	reduced echelon form Mathematics A matrix is in reduced echelon form if it is in echelon form and, further, every column that contains a leading 1 (of some row) otherwise has entries of 0. For example, these two matrices are in reduced echelon form: $[\begin{matrix} 1 & 6 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & - 3 \\ 0 & 0 & 0 & 1 & 5 \end{matrix}], [\begin{matrix} 0 & 0 & - 1 & 4 & 2 \\ 0 & 1 & 2 & - 3 & 5 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}] .$ Any matrix can be transformed to a unique matrix in reduced echelon form using elementary row operations, by Gauss–Jordan elimination. The solutions of a system of linear equations can be immediately obtained from the reduced echelon form to which the augmented matrix has been transformed.
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