Question
Download Solution PDFFind the eigenvalue for the matrix
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values.
- For a square matrix A, an Eigenvector(X) and Eigenvalue(λ) make this equation true i.e., AX = λX.
- For eigen values, |A - λ × I| = 0
Calculation:
Given:
|A - λI| = 0
⇒
⇒ (4 - λ)[(3 - λ)(5 - λ) -0] - 1[5 - λ - 2] + 3[0 - 2(3 - λ)] = 0
⇒ (4 - λ)(3 - λ)(5 -λ) - 3 + λ - 18 + 6λ = 0
⇒
⇒
By hit and trial method, At λ = 3, The above equation becomes zero
So, (λ - 3) is the factor of the above equation.
∴ (λ - 3) (λ2 - 9λ + 13) = 0
⇒ λ = 3,
7.1 is only in the option so (3) is correct
Last updated on May 9, 2025
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