search
Log In
6 votes
653 views

in Linear Algebra 653 views

1 Answer

9 votes
 
Best answer

The characteristic equation can be rewritten as :

          λ3  +  2 λ2  + 2 λ + 1  =  0

==>   λ ( λ2  +  2 λ + 1)  + 1(λ + 1)  =  0

==>    λ (λ + 1)2  + 1(λ + 1)  =  0

==>    (λ + 1) (λ+ λ + 1)   =  0 

Solving which we get λ = -1 , ω  , ω2  where ω  , ωare cube roots of unity ..

As we know :

Modulus of each of cube roots of unity  =  | ω |  =  | ω|  =  1

Also we know , 

Eigen values of matrix satisfies the corresponding characteristic equation and if all eigen values have modulus value = 1 , then the matrix is said to be orthogonal.

which is the case here..

Hence C) is the correct answer.. 


selected by
0
Could you please elucidate further? Thank you in advance.
0
didnt get it

Related questions

0 votes
0 answers
2
1.5k views
I have learned a shortcut for finding eigen values and characteristic equation. It is as follows. $\lambda ^{_{3}}- \alpha \lambda ^{2}+ \beta \lambda - \gamma =0$ where $ \alpha =$ trace of 3*3 matrix $ \beta =$ ... in the below problem I'm stuck, Could any one help me find why I'm stuck . I was getting answer using this trick for almost all problems
asked May 2, 2016 in Linear Algebra pC 1.5k views
0 votes
0 answers
3
172 views
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$ Then find them, $1)$ Eigen Values $2)$ Trace of the matrix$=$Sum of Leading Diagonal Elements$=\sum a_{ij},$ where $i=j$ $3)Det(A)$
asked Oct 25, 2018 in Linear Algebra Lakshman Patel RJIT 172 views
5 votes
1 answer
4
387 views
A 3× 3 real matrix has an eigen value i, then its other two eigen values can be (A) 0, 1. (B) -1, i. (C) 2i, -2i. (D) 0, -i.
asked Nov 14, 2017 in Mathematical Logic Lakshman Patel RJIT 387 views
...