由 訪客 於 星期三 九月 17, 2008 4:46 amAnonymous 寫到:各位大大好
我不懂的題目如下
find the eigenvalues and eigenvectors for the following 2 X 2 matrices
|2 , -1|
a= |1 , 4 |
|-4 , -6|
b= |3 , 5|
但我不知道答案是什麼?
有大大知道嗎?
非常感謝
det(a-tI)=|2-t -1| =(2-t)(4-t)+1=t^2-6t+8+1=t^2-6t+9=(t-3)^2
|1 4-t |
Thus,the eigenvalue is 3 of multiplicity 2.
Solve (a-3I)X=0,X=(x,y)
=>[-1 -1 |0]->[1 1|0]
[ 1 1 |0] [0 0|0]
So X=t(-1,1) is an eigenvector corresponding to 3,where t belonging to R.
b類似