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GATE EC 2024 Set 1 — Question 30

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NAT+1 / -0EasyVector Spaces, Basis & DimensionLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Vector Spaces, Basis & Dimension

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Question

Let R\mathbb{R} and R3\mathbb{R}^3 denote the set of real numbers and the three dimensional vector space over it, respectively. The value of α\alpha for which the set of vectors{[2−3α],[3−13],[1−57]}\{[2 \quad -3 \quad \alpha], [3 \quad -1 \quad 3], [1 \quad -5 \quad 7]\}does not form a basis of R3\mathbb{R}^3 is _______.
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