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Let \(A\) be a real symmetric matrix. \(\lambda_1,\lambda_2\;(\lambda_1\neq\lambda_2)\) be two eigen values of \(A\) and \(X_1,X_2\) are respectively the eigen vectors of \(A\) corresponding to \(\lambda_1\) and \(\lambda_2\), then \(X_1^TX_2=\)

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For every real symmetric matrix, eigenvectors corresponding to distinct eigenvalues are always orthogonal. This property is frequently used in linear algebra and matrix theory problems.

Updated On: Jul 23, 2026

\(X_2^TX_1\neq 0\)
\(X_1X_2^TX_1=0\)
\(X_2X_1^TX_2=0\)
\(X_2^TX_1=0\)

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The Correct Option is D

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Let \(A\) be a real symmetric matrix. \(\lambda_1,\lambda_2\;(\lambda_1\neq\lambda_2)\) be two eigen values of \(A\) and \(X_1,X_2\) are respectively the eigen vectors of \(A\) corresponding to \(\lambda_1\) and \(\lambda_2\), then \(X_1^TX_2=\)

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The Correct Option is D

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