Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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
#SPJ4
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
