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GO Classes | CSE/DA Course | Linear Algebra

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Which of the following conditions imply that matrix $\mathbf{A}$ of size $n \times n$ is invertible?

  1. only $\operatorname{rank}(\mathbf{A})=n$
  2. only $\mathbf{A} \vec{x}=0 \Leftrightarrow \vec{x}=0$
  3. only $\operatorname{det}(\mathbf{A}) \neq 0$
  4. All of these

3 Answers

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All 3 options A,B,C implies that column of A are LI = n

So ans is D

 

 
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If a matrix is square and invertible, it means it has full rank.
For a square matrix, having full rank implies that the system has only the trivial solution, and this also means that the determinant is non-zero.

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