If the columns of an $n \times n$ matrix are linearly independent, then the columns span $\mathbb{R}^{n}$ My textbook says that its true but I can't find a proof of this on the internet.

&quot;If $A$ is an $n \times n$ matrix with linearly independent columns, then the columns of $A$ span $\mathbb{R}^{n}$.&quot;
The dimension of a finite dimensional vector space is the maximal number of linearly independent vectors, and it is also the minimal number of a system of generators. A maximal system of linearly independent vectors is a basis. A minimal system of generators is a basis.
The dimension of a finite dimensional vector space is the maximal number of linearly independent vectors, and it is also the minimal number of a system of generators. A maximal system of linearly independent vectors is a basis. A minimal system of generators is a basis.