Engineering Mathematics · Linear Algebra
Official IIT answer key · IIT Guwahati · Audited Aug 2026
GATE CSE 2018 Q26 · MCQ · 2 marks
Key concept
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Topic notes
Linear Algebra in GATE CS is consistently tested across fundamental properties of matrices, systems of linear equations, and spectral theory (eigenvalues and eigenvectors). Questions heavily leverage algebraic identities such as trace-sum, determinant-product relations, rank-nullity theorem, and structural properties like orthogonality of symmetric matrices and LU decomposition. Problems frequently appear as 1-mark and 2-mark conceptual MCQs/MSQs or direct numerical computation NATs.
Full Linear Algebra guide →Consider a matrix P whose only eigenvectors are the multiples of bmatrix 1 \\ 4 bmatrix. Consider the following statements. (I) P does not have an inverse (II) P has a repeated eigenvalue (III) P cannot be diagonalized Which one of the following options is correct?
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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.
