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Q#1 Linear Algebra GATE CH 2024 MSQ +1 mark -0 marks

Consider a linear homogeneous system of equations \(Ax = 0\), where A is an đť‘›×đť‘› matrix, x is an đť‘›×1 vector and 0 is an đť‘›×1 null vector. Let 𝑟 be the rank of A. For a non-trivial solution to exist, which of the following conditions is/are satisfied?

r < n

Determinant of A = 0

r = n

Determinant of A ≠ 0

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