矩阵变换求矩阵的秩 (2 -1 -1 1 2) (1 1 -2 1 4) (4 -6 2 -矩阵变换求矩阵的秩(2 -1 -1 1 2)(1 1 -2 1 4)(4 -6 2 -2 4)(3 6 -9 7 9)怎么求秩,有些矩阵变换好难想到
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![矩阵变换求矩阵的秩 (2 -1 -1 1 2) (1 1 -2 1 4) (4 -6 2 -矩阵变换求矩阵的秩(2 -1 -1 1 2)(1 1 -2 1 4)(4 -6 2 -2 4)(3 6 -9 7 9)怎么求秩,有些矩阵变换好难想到](/uploads/image/z/6944194-10-4.jpg?t=%E7%9F%A9%E9%98%B5%E5%8F%98%E6%8D%A2%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9+%EF%BC%882+-1+-1+1+2%EF%BC%89+%EF%BC%881+1+-2+1+4%EF%BC%89+%EF%BC%884+-6+2+-%E7%9F%A9%E9%98%B5%E5%8F%98%E6%8D%A2%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9%EF%BC%882+-1+-1+1+2%EF%BC%89%EF%BC%881+1+-2+1+4%EF%BC%89%EF%BC%884+-6+2+-2+4%EF%BC%89%EF%BC%883+6+-9+7+9%EF%BC%89%E6%80%8E%E4%B9%88%E6%B1%82%E7%A7%A9%2C%E6%9C%89%E4%BA%9B%E7%9F%A9%E9%98%B5%E5%8F%98%E6%8D%A2%E5%A5%BD%E9%9A%BE%E6%83%B3%E5%88%B0)
矩阵变换求矩阵的秩 (2 -1 -1 1 2) (1 1 -2 1 4) (4 -6 2 -矩阵变换求矩阵的秩(2 -1 -1 1 2)(1 1 -2 1 4)(4 -6 2 -2 4)(3 6 -9 7 9)怎么求秩,有些矩阵变换好难想到
矩阵变换求矩阵的秩 (2 -1 -1 1 2) (1 1 -2 1 4) (4 -6 2 -
矩阵变换求矩阵的秩
(2 -1 -1 1 2)
(1 1 -2 1 4)
(4 -6 2 -2 4)
(3 6 -9 7 9)
怎么求秩,有些矩阵变换好难想到
矩阵变换求矩阵的秩 (2 -1 -1 1 2) (1 1 -2 1 4) (4 -6 2 -矩阵变换求矩阵的秩(2 -1 -1 1 2)(1 1 -2 1 4)(4 -6 2 -2 4)(3 6 -9 7 9)怎么求秩,有些矩阵变换好难想到
一、把矩阵A视为列向量,写成列向量组成的矩阵:
2,1,4,3,
-1,1,-6,6,
-1,-2,2,-9,
1,1,-2,7,
2,4,4,9,
二、交换第1行和第4行,不改变矩阵的秩:
1,1,-2,7,
-1,1,-6,6,
-1,-2,2,-9,
2,1,4,3,
2,4,4,9,
三、使用初等行变换,将矩阵进行运算:
把第一行加到第二行;把第一行加到第三行;把第一行乘以-2再加到第四行;把第一行乘以-2,再加到第五行,从而使得第一列的后几个元素为0:
1,1,-2,7,
0,2,-8,13,
0,-1,0,-6,
0,-1,8,-11,
0,2,8,-5,
四、继续进行行变换,把第二行乘以0.5再加到第三行,也加到第四行;把第二行乘以-1再加到第五行:
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,4,-4.5,
0,0,16,-18,
五、把第三行加到第四行上,把4倍第三行加到第五行上:
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,-16,
六、把-4倍第四行加到第五行:
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
七、先1/2倍第二行,再去减第一行:
1,0,2,0.5,
0,1,-4,6.5,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
八、用第三行去减第二行:
1,0,2,0.5,
0,1,0,6,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
九、-1/4倍第三行,-1/4倍第四行:
1,0,2,0.5,
0,1,0,6,
0,0,1,-0.125,
0,0,0,1,
0,0,0,0,
十、2倍第三行去减第一行:
1,0,0,0.75,
0,1,0,6,
0,0,1,-0.125,
0,0,0,1,
0,0,0,0.
十一、矩阵经初等变换转化为阶梯矩阵后 非零行个数即为矩阵的秩,故秩为4;因为 4=秩