Question

Determine the Eigen values for the matrix A = \begin{pmatrix} 1 & -3 & 3 \\ 3 & -5 & 3 \\ 6 & -6 & 4 \end{pmatrix} ​⎝ ​⎛ ​​ ​1 ​3 ​6 ​​ ​−3 ​−5 ​−6 ​​ ​3 ​3 ​4 ​​ ​⎠ ​⎞ ​​ .

Answer 1

Answer:

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Answer 2

Answer:

The eigenvalues for the matrix

     $A = \begin{pmatrix}1&-3&3\\3&-5&3\\6&-6&4\end{pmatrix}$

are λ = 7 and λ = 1.

Step-by-step explanation:

Now, we determine the eigenvalues of the matrix A,

$A = \begin{pmatrix}1&-3&3\\3&-5&3\\6&-6&4\end{pmatrix}$

we need to solve the characteristic equation det(A - λI) = 0,

where denotes an eigenvalue and I denote the identity matrix.

The determinant can be calculated as follows:

$det(A - \lambda I) = \begin{vmatrix} 1-\lambda & -3 & 3 \\ 3 & -5-\lambda & 3 \\ 6 & -6 & 4-\lambda \end{vmatrix}$

Expanding this determinant, we get:

det(A - λI) = (1-λ)((-5-λ)(4-λ) - 33) - 33×(3) + 3×(-6)×(3)

det(A - λI) = (1-λ)((4-λ)² - 9) - 9 + 9

det(A - λI) = (1-λ)((4-λ)² - 9) = 0

⇒ (1-λ)((4-λ)² - 9) = 0

Now, we need to solve the quadratic equation (4-λ)^2 - 9 = 0, which gives us:

⇒ (4-λ)² = 9

⇒ 4-λ = ±3

⇒ λ = 4 ± 3

So, the eigenvalues of matrix A are λ = 7 and λ = 1.

To learn more about eigenvalues, click on the link below:

https://brainly.in/question/33499954

To learn more about determinants, click on the link below:

https://brainly.in/question/2797180

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