Question

Give an example of a 2x2 matrix without any real eigenvalues:___________

Answer 1

Answer:

Step-by-step explanation:

An eigenvalue of n × n is a function of a scalar $\lambda$  considering that there is a solution (i.e. nontrivial) to an eigenvector x of Ax =  

Suppose the matrix $A = \left[\begin{array}{cc}-1&-1\\2&1\\ \end{array}\right]$

Thus, the equation of the determinant (A - $\lambda$1) = 0

This implies that:

$\left[\begin{array}{cc}-1-\lambda &-1\\2&1- \lambda\\ \end{array}\right] =0$

$-(1 - \lambda^2 ) + 2 = 0$

$-1 + \lambda ^2 + 2= 0$

$\lambda^2 +1 =0$

Hence, the eigenvalues of the equation are $\mathtt{\lambda = i , -i}$

Also, the eigenvalues can be said to be complex numbers.