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Sagot :
The eigenvalues of A are 5 and 10.
What is  eigenvalues ?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
The eigenvalues of the 2 x 2 matrix are described by the following characteristic polynomial:
[tex]$t^2-{tr}(A) \cdot t+{det}(A)=0$[/tex]
The roots of the characteristic polynomial are deflned by the quadratic formula:
[tex]t=\frac{{tr}(A) \pm \sqrt{[{tr}(A)]^2-4-{det}(A)}}{2} \text { (2) }$[/tex]
If we know that [tex]${tr}(A)=15$[/tex]and [tex]${det}(A)=50$[/tex], then the elgenvalues of A are:
[tex]$\begin{aligned}& t=\frac{15 \pm \sqrt{15^2-4 \cdot(50)}}{2} \\& t_1=10 \vee t_2=5\end{aligned}$[/tex]
To learn more about eigenvalues visit:https://brainly.com/question/29579848
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