# [SOLVED]307 Construct 3 different 2x2 matrices

#### karush

##### Well-known member
Construct 3 different $2\times2$ matrices
1. having two distinct real eigenvalues,
$A=\begin{bmatrix} 2 & -1\\ -1& 2 \end{bmatrix},\quad \left| \begin{array}{rr} 2 - \lambda & -1 \\ -1 & 2 - \lambda \end{array} \right|=\lambda^{2} - 4 \lambda + 3 \therefore \lambda_1=3\ \lambda_2=1$

2. a pair of complex eigenvalues.
$\left| \begin{array}{cc} 2 - \lambda & 1 \\ -1 & 2 - \lambda \end{array} \right|=\lambda^{2} - 4 \lambda + 5\quad \lambda_{1}=2 - i,\lambda_{1}=2 + i$

3. two identical real eigenvalues,

ok hopefully 1 and 2 are ok

on 3 I was just going to do this $(\lambda-2)(\lambda-2)$
and go backwards to a matrix but ?????