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Best answer
35 votes
35 votes
For finding the Eigen Values of a Matrix we need to build the Characteristic equation which is of the form,
$$A-\lambda I$$
where $A$ is the given Matrix, $\lambda$ is a constant, $I$ is the identity matrix.

We'll have a Linear equation after solving $A-\lambda I,$ which will give us two roots for $\lambda.$

$(4 - \lambda) (1 - \lambda) -10 = 0$
$\implies 4 - 5 \lambda+\lambda^2 = 10$
$\implies\lambda^2 - 5\lambda -6 = 0$
$\implies (\lambda - 6)(\lambda +1) = 0$
$\implies \lambda = -1,6.$

$6$ is larger and hence the required answer.
edited by
7 votes
7 votes
Sum of eigen values= Trace of matrix= 4+1=5

Product of eigen values= Determinant= 4*1-5*2=-6

We can easily find two eigen values using results above

6 and -1.
Answer:

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