Chemical Engineering > GATE 2024 > Linear Algebra
Consider a linear homogeneous system of equations Ax = 0, where A is an 𝑛 Γ— 𝑛 matrix, x is an 𝑛 Γ— 1 vector and 0 is an 𝑛 Γ— 1 null vector. Let π‘Ÿ be the rank of A. For a non-trivial solution to exist, which of the following conditions is/are satisfied?
A
Determinant of A=0
B
r=n
C
r
D
Determinant of A≠0

Correct : a, c

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linear homogeneous system rank of matrix null vector GATE Chemical Engineering 2024 determinant matrix chemical engineering gate system of equations GATE 2024 questions

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