python - 如何同情矩阵等级 nessesary 值？

Question

    from sympy import *
    var('a11 a12 a13 a21 a22 a23 a31 a32 a33')
    print("(1)",
          Matrix([[-1, 1, -1], [2, 0, 1], [1, -3, 2]])
          .rank()
         )
    print("(2)",
          Matrix([[a11,a12,a13],[a21,a22,a23],[a31,a32,a33]])
          .subs({a11:-1,a12:1,a13:-1,a21:2,a22:0,a23:1,a31:1,a32:-3,a33:2})
          .rank()
         )
    print("(3)",
          Matrix([[a11,a12,a13],[a21,a22,a23],[a31,a32,a33]])
          .rank()
         )
    print("(4)",
          Matrix([[a11,a12,a13],[a21,a22,a23],[a31,a32,a33]])
          .rank()
          .subs({a11:-1,a12:1,a13:-1,a21:2,a22:0,a23:1,a31:1,a32:-3,a33:2})
         )

(1) 2

(2) 2

为什么（3）排名= 3？

为什么（4）AttributeError？

文件“C:/Users/xxx/PycharmProjects/pythonProject/main.py”，第 17 行，在 Matrix([[a11,a12,a13],[a21,a22,a23],[a31,a32,a33]]) AttributeError：“int”对象没有属性“subs”

标签： pythonmatrixsympy