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GATE ME 2014 Set 3 — Question 11

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MCQ+1 / -0.33EasyEigenvalues & EigenvectorsLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors

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Question

Consider a 3×33 \times 3 real symmetric matrix SS such that two of its eigenvalues are a≠0,b≠0a \neq 0, b \neq 0 with respective eigenvectors [x1x2x3],[y1y2y3]\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}, \begin{bmatrix} y_1 \\ y_2 \\ y_3 \end{bmatrix}. If a≠ba \neq b then x1y1+x2y2+x3y3x_1y_1 + x_2y_2 + x_3y_3 equals
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