Question
Determining Eigenvalues of a matrix :
A. Solve the characteristic equation
B. Form matrix $A - \lambda I$
C. Compute determinant
D. Identify eigenvalues
Choose the correct answer from the options given below :
This question was previously asked in
CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
The correct answer is
B, C, A, D
Eigenvalue Calculation Steps
To determine the eigenvalues of a matrix A, follow these sequential steps:
- Form the matrix $A - \lambda I$: Subtract the scalar $\lambda$ (lambda) multiplied by the identity matrix I from the original matrix A. This results in a new matrix where $\lambda$ is a variable.
- Compute determinant: Calculate the determinant of the matrix formed in the previous step, $\det(A - \lambda I)$. This determinant will be a polynomial in $\lambda$, known as the characteristic polynomial.
- Solve the characteristic equation: Set the characteristic polynomial equal to zero: $\det(A - \lambda I) = 0$. Solving this equation for $\lambda$ yields the eigenvalues.
- Identify eigenvalues: The values of $\lambda$ obtained by solving the characteristic equation are the eigenvalues of the matrix A.
Therefore, the correct sequence for determining the eigenvalues of a matrix is:
- B. Form matrix $A - \lambda I$
- C. Compute determinant
- A. Solve the characteristic equation
- D. Identify eigenvalues
This corresponds to the order B, C, A, D.
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