Question:medium

If \( \lambda_1, \lambda_2 \) and \( \lambda_3 \) are the eigen values of a square matrix \( A \), then the eigen values of \( A^{-1} + 2I + A \) are

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If \( \lambda \) is an eigenvalue of a matrix \( A \), then any matrix polynomial or functional expression \( f(A) \) will have corresponding eigenvalues given directly by substituting \( \lambda \) into the function, resulting in \( f(\lambda) \).
Updated On: Jul 9, 2026
  • \( \frac{1}{\lambda_1} + 2 + \lambda_1 \), \( \frac{1}{\lambda_2} + 2 + \lambda_2 \) and \( \frac{1}{\lambda_3} + 2 - \lambda_3 \)
  • \( \frac{1}{\lambda_1} + 2 + \lambda_1 \), \( \frac{1}{\lambda_2} - 2 - \lambda_2 \) and \( \frac{1}{\lambda_3} - 2 - \lambda_3 \)
  • \( \frac{1}{\lambda_1} - 2 - \lambda_1 \), \( \frac{1}{\lambda_2} - 2 - \lambda_2 \) and \( \frac{1}{\lambda_3} - 2 - \lambda_3 \)
  • \( \frac{1}{\lambda_1} + 2 + \lambda_1 \), \( \frac{1}{\lambda_2} + 2 + \lambda_2 \) and \( \frac{1}{\lambda_3} + 2 + \lambda_3 \)
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The Correct Option is D

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