→ cha122977:第二題答案是是det(A)=±1嗎? 10/31 13:18
→ trainausidd:很抱歉 無解答... 10/31 13:37
推 simy:第一題 a=60吧 11/01 19:00
64 8 -10
1.for A = [ 8 76 -20 ] with eigenvalues 30, 60, and 90 ,
-10 -20 40
find a real 3x1 vector y and a real number a
A y
such that the matrix [ ] has eigenvalues 20 , 40 , 80 ,and 100 .
y^T a
(y^T means the transpose of the vector y )
2.Find all n by n matrices A satisfying the matrix equality A^3+A^2-A-I=0
0 1
3.Does the matrix A = [ ] have a complex square root C such that C^2 = A ?
-1 0
Does A have a real square root R such that R^2 = A ?
To each question , if the answer is positive ,
then derive a proper square root. otherwise show the non-existence.
以上是原題,麻煩各位大大幫忙解惑 謝謝
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