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GATE ME 2017 Set 2 — Question 28

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NAT+1 / -0MediumEigenvalues & EigenvectorsLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors

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Consider the matrix A=[50707080]A = \begin{bmatrix} 50 & 70 \\ 70 & 80 \end{bmatrix} whose eigenvectors corresponding to eigenvalues λ1\lambda_1 and λ2\lambda_2 are x1=[70λ1−50]x_1 = \begin{bmatrix} 70 \\ \lambda_1 - 50 \end{bmatrix} and x2=[λ2−8070]x_2 = \begin{bmatrix} \lambda_2 - 80 \\ 70 \end{bmatrix}, respectively. The value of x1Tx2x_1^T x_2 is ________.
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