线性代数,这个题怎么做那个F(X)的.怎么消呢?
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线性代数,这个题怎么做那个F(X)的.怎么消呢?
![](http://img.wesiedu.com/upload/b/c6/bc63ea5b66ff676b708a86d780e990b4.jpg)
![](http://img.wesiedu.com/upload/b/c6/bc63ea5b66ff676b708a86d780e990b4.jpg)
![线性代数,这个题怎么做那个F(X)的.怎么消呢?](/uploads/image/z/8849032-16-2.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%2C%E8%BF%99%E4%B8%AA%E9%A2%98%E6%80%8E%E4%B9%88%E5%81%9A%E9%82%A3%E4%B8%AAF%EF%BC%88X%EF%BC%89%E7%9A%84.%E6%80%8E%E4%B9%88%E6%B6%88%E5%91%A2%3F)
f(x)=
[ x-2 x-1 x-2 x-3 ]
[ 2x-2 2x-1 2x-2 2x-3]
[ 3x-3 3x-2 4x-5 3x-5]
[ 4x 4x-3 5x-7 4x-3]
c2-c1,c3-c1 ,c4-c1,c4-c2:
[ x-2 1 0 0]
[ 2x-2 1 0 0]
[ 3x-3 1 x-2 -1]
[ 4 x -3 x-7 -6]
=(x-2-2x+2)(-6x+12+x-7)
=(-x)(-5x+5)
=5x^2-5x
∴f(x)=0的根为:x=0 x=1
[ x-2 x-1 x-2 x-3 ]
[ 2x-2 2x-1 2x-2 2x-3]
[ 3x-3 3x-2 4x-5 3x-5]
[ 4x 4x-3 5x-7 4x-3]
c2-c1,c3-c1 ,c4-c1,c4-c2:
[ x-2 1 0 0]
[ 2x-2 1 0 0]
[ 3x-3 1 x-2 -1]
[ 4 x -3 x-7 -6]
=(x-2-2x+2)(-6x+12+x-7)
=(-x)(-5x+5)
=5x^2-5x
∴f(x)=0的根为:x=0 x=1