在给定的矩阵中，特征值之一是 1。特征值 1 对应的特征向量是
⎡ 1 -1 2 ⎤
⎢ 0 1 0 ⎥
⎣ 1 2 1 ⎦_%7C_Question_65_0.jpg){kind=small}
(一) A
(乙)乙
(C)丙
(四)丁答案：(乙)
说明：让 z 代表特征值。
And let the given matrix be A (square matrix of order 3 x3)
The characteristic equation for this is :
AX = zX ( X is the required eigenvector )
AX - zX = 0
[ A - z I ] [X] = 0 ( I is an identity matrix of order 3 )
put z = 1 ( because one of the eigenvalue is 1 )
[ A - 1 I ] [X] = 0
The resultant matrix is :
[ 0 -1 2 ] [x1] [0]
| 0 0 0 ] |x2] =|0|
[ 1 2 0 ] |x3] [0]
Multiplying thr above matrices and getting the equations as:
-x2 + 2x3 = 0 ----------------(1)
x1 + 2x2 = 0-----------------(2)
now let x1 = k, then x2 and x3 will be -k/2 and -k/4
respectively.
hence eigenvector X = { (k , -k/2, -k/4) } where k != 0
put k = -4c ( c is also a constant, not equal to zero ),
we get X = { ( -4c, 2c, 1c ) }, i.e. { c ( -4, 2, 1 ) }
Hence option B.这个问题的测验