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Consider a linear homogeneous system of equations \( Ax = 0 \), where \( A \) is an \( n \times n \) matrix, \( x \) is an \( n \times 1 \) vector, and \( 0 \) is an \( n \times 1 \) null vector. Let \( r \) be the rank of \( A \). For a non-trivial solution to exist, which of the following conditions is/are satisfied?
Consider a linear homogeneous system of equations \( Ax = 0 \), where \( A \) is an \( n \times n \) matrix, \( x \) is an \( n \times 1 \) vector, and \( 0 \) is an \( n \times 1 \) null vector. Let \( r \) be the rank of \( A \). For a non-trivial solution to exist, which of the following conditions is/are satisfied?
Updated On: Jul 17, 2024
- Determinant of \( A = 0 \)
- \( r = n \)
- \( r < n \)
- Determinant of \( A \) \(\neq\)\( 0 \)
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The Correct Option is A, C
Solution and Explanation
The correct Answer are (A) :Determinant of \( A = 0 \), (C):\( r < n \)
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