证明：|x00α0||-1x0α1||0-1xα2||00-1x+α3|=x4+α3x3+α2x1+α1x+α0．
2024-08-15线性代数(02198)
证明：
|x00α0|
|-1x0α1|
|0-1xα2|
|00-1x+α3|
=x4+α3x3+α2x1+α1x+α0．
【正确答案】：证明： |x 0 0 α | |-1 x 0 α1 | |0 -1 x α2 | |0 0 -1 x+α3| = |0 0 0 α0+α1x+α2x2+x4+α3x3 |1 0 0 α1+α2x+x3+α3x2 |0 -1 0 α2+x2+α3x |0 0 -1 x+α3 =(-1)1+4(α0+α1x+α2x2+x4+α3x3) |-1 0 0| |0 -1 0| |0 0 -1| =x0+α3 x3+α2 x2+α1 x+α0 ．
|x00α0|
|-1x0α1|
|0-1xα2|
|00-1x+α3|
=x4+α3x3+α2x1+α1x+α0．
【正确答案】：证明： |x 0 0 α | |-1 x 0 α1 | |0 -1 x α2 | |0 0 -1 x+α3| = |0 0 0 α0+α1x+α2x2+x4+α3x3 |1 0 0 α1+α2x+x3+α3x2 |0 -1 0 α2+x2+α3x |0 0 -1 x+α3 =(-1)1+4(α0+α1x+α2x2+x4+α3x3) |-1 0 0| |0 -1 0| |0 0 -1| =x0+α3 x3+α2 x2+α1 x+α0 ．
