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Chapter 1 linear equation [P2] 线性方程 coefficient [P2] 系数 constant term [讲义‐P1] 常数（项） systems of linear equations (linear system) [P3] 线性方程组 solution [P3] 解 solution set [P3] 解集 tuple [P3] 数组 equivalent [P3] 等价 equivalent system [P3] 等价系统，等价方程组 consistent [P4] 相容 inconsistent [P4] 不相容 consistent linear system 相容（有解）的线性方程组inconsistent linear system 不相容（无解）的线性方程组coefficient matrix [P5] 系数矩阵 augmented matrix [P5] 增广矩阵 elementary operations [P7] 初等变换 elementary row operation [P7] 初等行变换 row equivalent [P7] 行等价（矩阵） equivalent matrix [讲义‐P3] 等价矩阵 Leading entry [P14] 先导元素 entry of matrix 矩阵的元素 echelon form (row echelon form) [P14] 阶梯形 reduced echelon form (reduced row echelon form) [P14] 简化阶梯形 Gaussian elimination [P14]脚注 高斯消元法 the elimination of variables 消元法 row reduced [P15] 行化简 pivot position [P16] 主元位置 pivot column [P16] 主元列 pivot [P17] 主元 forward phase [P20] 自上（向下）阶段 backward phase [P20] 自下（向上）阶段 basic variable [P20] 基本变元 free variable [P20] 自由变元 general solution [P21] 一般解，通解 back‐substitution [P22] 回代法，侧转代入 vector [P28] 向量， 矢量 scalar [P28] 数量，纯量， 无向量 parallelogram rule [P30] 平行四边形法则 linear combination [P32] 线性组合 generated (spanned) [P35] 生成(张成) product [P45] 乘积 homogeneous systems [P50] 齐次系统，齐次线性方程组 trivial solution [P50] 平凡解，零解 nontrivial solution [P51] 非平凡解， 非零解 parametric vector form [P52] 参数向量形式 nonhomogeneous systems [P50] 非齐次线性方程组 linear independent [p65] 线性相关 linearly independent [P65] 线性无关 linear transformation [P73] 线性变换 domain [P73] 值域 shear transformation [P76] 剪切变换 contraction [P77] 压缩变换 dilation [P77] 拉伸变换