# Can a $2 \times 3$ matrix be full rank?

I have been watching 3blue1brown's Essence of Linear Algebra series on youtube, and I have a question about $$2 \times 3$$ matrices. For example: $$\begin{bmatrix}3&1&4\\1&5&9\end{bmatrix}$$

Although the basis vectors are linearly independent, the matrix transforms 3D space into 2D space. Thus, would this matrix be considered full rank or not?

• What do you mean by "full rank" here? The matrix has rank $2$, which is the largest possible rank for a $2\times 3$ matrix. – David C. Ullrich Nov 23 '18 at 16:31
• This is purely a matter of semantics: how have you defined "full rank"? – user3482749 Nov 23 '18 at 16:37