1) for each of the following matrices , find the characteristic equation , the e

Question

1) for each of the following matrices , find the characteristic equation , the eigenvalues,and corresponding eigenvectors and eigenspaces and give a matrix P such the matrix P^...1 AP is diagonal,or explain why this is not possible

ii) A= [1 2 0]
[-3 2 3]
[-1 2 2]

Explanation / Answer

for characteristic eqn we have det[A-?I]=0 [2-? 12 -8] [0 -8 -? 6] =0 [0 -9 7-?] solving which we get the characteristic eqn (2-?)[(-8-? )(7-?)+9*6]=0 =>(2-?)(?^2 -7?+8?-56+54)=0 =>(2-?)(?^2+?-2)=0 =>(2-?)(?+2)(?-1)=0 the eigen values are ?=-2,1,2 eigen spaces are for ?=1 [1 12 -8] [0 -9 6] [0 -9 6] similarly putting values of ? =-2 and 2 we get the required eigenspaces please rate my answer,Thank you

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.