Nullity of Matrix A: Implications & Null Space Span

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A matrix A with a nullity of 1 implies that its null space is spanned by a single vector, which varies depending on the specific matrix. This characteristic indicates that the matrix is not invertible. Additionally, the eigenvalue 0 is present, with a geometric multiplicity of 1. These properties highlight the limitations in the matrix's ability to transform space. Understanding these implications is crucial for analyzing matrix behavior in linear algebra.
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For a matrix A, if its nullity is equal to 1, what is the implication of that? What spans its null space?

Thanks a lot!
 
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The null space of a nullity 1 matrix is spanned by a single vector. What that vector is depends on the matrix.
 
Some easy implications are that the matrix will not be invertible. Moreover, A will have 0 has an eigenvalue and the geometric multiplicty of 0 will be 1.
 

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