三个线性方程组的增广矩阵的行阶梯形 𝑥 ， 𝑦 和 𝑧 下面列出。 对于每个增广矩阵， 𝐴 ， 𝐵 和 𝐶 下列哪个选项正确描述了相应线性方程组的解的个数？ [ 1 0 0 | 0 0 1 0 | 0 0 0 0 | 1 ] ⏟ 𝐴 [ 1 0 0 | 0 0 1 0 | 1 0 0 1 | 1 ] ⏟ 𝐵 [ 1 0 0 | − 2 0 1 0 | − 3 0 0 0 | 0 ] ⏟ 𝐶单项选择题

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类似问题

The system of linear equations \[\begin{eqnarray}2x_1 + 3x_2 + x_3 + x_5 &=& -1 \\-4x_1 -6x_2 -2x_3-4x_4+18x_5 &=& 26 \\10x_1 + 15x_2 +5x_3 - x_4 + 10x_5 &=& 1\end{eqnarray}\] has row echelon form \[\left[\begin{array}{rrrrr|r}2 & 3 & 1 & 0 & 1 & -1 \\0 & 0 & 0 & -1 & 5 & 6 \\0 & 0 & 0 & 0 & 0 & 0\end{array}\right].\] How many solutions does this system have?

Which of the following matrices is in row echelon form (choose one or more)?

Which of the following matrices is in row echelon form (choose one or more)?

Row echelon forms of the augmented matrices for three systems of linear equations in 𝑥 , 𝑦 and 𝑧 are given below. For each augmented matrix, 𝐴 , 𝐵 and 𝐶 , which of the following options correctly describes the number of solutions to the corresponding system of linear equations? [ 1 0 0 | 2 0 1 0 | 0 0 0 1 | − 1 ] ⏟ 𝐴 [ 1 0 0 | − 2 0 0 0 | 0 0 0 0 | 0 ] ⏟ 𝐵 [ 1 0 0 | 0 0 1 0 | 4 0 0 0 | − 2 ] ⏟ 𝐶

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