For the given matrix find its characteristic polynomial and...

For the given matrix find its characteristic polynomial and Eigenvalues. 9. A = egin{bmatrix} 0 & 1 -2 & -3 end{bmatrix} 10. A = egin{bmatrix} 5 & 0 & 0 1 & 2 & 1 1 & 1 & 2 end{bmatrix}

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 Hi from the question given that from the given matrix a is equal to 0 1 minus 2 minus 3.

00:11 So here we need to write the characteristic polynomial and the eigenvalues.

00:17 So characteristic polynomial is a minus lambda i is equal to 0.

00:21 So determinant of minus lambda 1 minus 2 minus 3 minus lambda is equal to 0.

00:31 So minus lambda times of minus 3 minus lambda plus 2 which is equal to 0.

00:38 For further simplification 3 lambda plus lambda square plus 2 is equal to 0.

00:45 Therefore the characteristic polynomial is lambda square plus 3 lambda plus 2 is equal to 0.

00:52 Now we need to find the eigenvalues.

00:55 So for further simplification first we need to factor out we have taken lambda square plus lambda plus 2 lambda plus 2 is equal to 0.

01:04 Then we factor out lambda times of lambda plus 1 plus 2 times of lambda plus 1 which is equal to 0.

01:11 So that the eigenvalues are lambda is equal to negative 1 and minus 2.

01:17 Now let us move on to the second question.

01:19 In the second question the given matrix a is 5 0 0 1 2 1 1 1 2.

01:39 Now we need to find the characteristic polynomial.

01:42 So a minus lambda i is equal to determinant of 5 minus lambda 0 0 1 2 minus lambda sorry 1 not 0.

01:55 So 1 1 1 2 minus lambda that could be equal to 0...

Question

For the given matrix find its characteristic polynomial and Eigenvalues. 9. A = egin{bmatrix} 0 & 1 -2 & -3 end{bmatrix} 10. A = egin{bmatrix} 5 & 0 & 0 1 & 2 & 1 1 & 1 & 2 end{bmatrix}

Please give Ace some feedback

For the given matrix find its characteristic polynomial and Eigenvalues. 9. A = egin{bmatrix} 0 & 1 -2 & -3 end{bmatrix} 10. A = egin{bmatrix} 5 & 0 & 0 1 & 2 & 1 1 & 1 & 2 end{bmatrix}