The solution space (null space) of a homogeneous linear system Ax=0 where A is a 3times4 matrix with text rank (A)=2 has dimension:

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SSC Pure Mathematics QUESTION #1279

Question 1

The solution space (null space) of a homogeneous linear system \(Ax=0\) where \(A\) is a \(3\times4\) matrix with \(\text{rank}(A)=2\) has dimension:

Correct Answer Explanation

By the Rank-Nullity Theorem: \(\dim(\text{null space}) = n - \text{rank}(A) = 4 - 2 = 2\).