Question

find eigen value of the matrix
(1 2) (1 2)
​

Answer 1

Answer:

Eigenvalues of the matrix  $\left[\begin{array}{ccc}1&2\\1&2\\\end{array}\right]$ = 0  and  3

Step-by-step explanation:

From the definition of the eigenvalue

let us consider the eigen value of the matrix is  λ.

then

              det(A - λI) = 0

              det(A - λ I ) = $\begin{vmatrix}1 - \lambda & 2\\1 & 2 - \lambda \\\end{vmatrix}$

                                 $= \lambda ^ 2-3\lambda \\= \lambda \cdot (\lambda -3)\\=0$

hence  either λ = 0 or (λ - 3) =0

if  λ  = 0 then we are done

if  λ - 3 = 0 this implies λ = 3

then

required eigenvalues are λ = 0 , 3

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