Question

矩阵→阶梯形矩阵→行最简→求秩

Answer 1

变换过程如下：

矩阵变化为3行不全为零的阶梯阵，所以：r（A）=3。

Answer 2

矩阵 A 初等行变换为
[1 -1 -3 0 3]
[2 1 0 1 2]
[2 3 4 2 0]
[3 1 -1 1 3]
初等行变换为
[1 -1 -3 0 3]
[0 3 6 1 -4]
[0 5 10 2 -6]
[0 4 8 1 -6]
初等行变换为
[1 -1 -3 0 3]
[0 -1 -2 0 2]
[0 5 10 2 -6]
[0 4 8 1 -6]
初等行变换为
[1 0 -1 0 1]
[0 -1 -2 0 2]
[0 0 0 2 4]
[0 0 0 1 2]
初等行变换为
[1 0 -1 0 1]
[0 1 2 0 -2]
[0 0 0 1 2]
[0 0 0 0 0]
r(A) = 3