GATE EE 2026 Set 1 — Question 49
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Engineering Mathematics → Linear Algebra → Matrix Algebra
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Question
Which one of the following statements is ALWAYS correct about a collection of column vectors, each having real-valued entries?
Correct answer
(A) If p n, then the column vectors must be linearly dependent
Solution
In a vector space of dimension (like ), the maximum number of linearly independent vectors is . Therefore, any set containing more than vectors () must be linearly dependent.
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