Matlab复习笔记

Posted 2021-06-28 akyna-zh

1.求极大线性无关组

A =

     1     2     3     1
     0     1     2    -2
     2     1     0     8

>> [R j] = rref(A)

R =

     1     0    -1     5
     0     1     2    -2
     0     0     0     0

%主元所在列数
j =

     1     2

//极大线性无关组
>> M = A(:,[1,2])

M =

     1     2
     0     1
     2     1

2.求Ax = 0基础解系

A =

     2    -2     1     3
     9    -5     2     8

%求出最小整数解
>> r = rank(A);
>> X = null(A, 'r')

X =

    0.1250   -0.1250
    0.6250    1.3750
    1.0000         0
         0    1.0000

%求出规范正交基
>> X = null(A)

X =

    0.1293   -0.1052
    0.3860    0.7386
    0.9041   -0.2092
   -0.1302    0.6322

3.左除与右除

右除正斜杠： A / B -> A * inv(B)
左除反斜杠： A \\ B -> inv(A) * B

4.求Ax = b特解：

A非方阵时，无法利用x = A^(-1) * b

应该使用x = A \\ b