Matrix product (notation in answer)

Question

Suppose I have a matrix $C=\begin{bmatrix} 1 & 0 \end{bmatrix}$ and a vector $\mathbf{x}=\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$.

I want to write the matrix product $C\mathbf{x}$, should the answer be vector notation (bold) or not?

I mean vector notation $$\mathbf{y}= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1 $$ or scalar notation $$ y= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1 $$ I use upright letters for matrices, bold letters for vectors. Non-bold for scalars.

Answer 1

$$C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=[x_1]$$ (note the brackets around $x_{1}$) is a

• $1 \times 1$ matrix, or
• a row vector of length one, or
• a column vector of length one,

you choose.