Writing the columns or Rows of a Matrix in Suffix Notation

Question

I have the following matrix:

$$M=\begin{bmatrix} a_1 & a_2 & a_3\\ b_1 & b_2 & b_3\\ c_1 & c_2 & c_3 \end{bmatrix} = \begin{bmatrix} \vec{a}\\ \vec{b}\\ \vec{c} \end{bmatrix}$$

and the following vectors:

$$\vec{a} = (a_1 , a_2 , a_3)\\ \vec{b} = (b_1 , b_2 , b_3)\\ \vec{a} = (c_1 , c_2 , c_3)$$

Is there a way to express this matrix in suffix notation using the vectors above?

Any hints?

Answer 1

I would write this as $$ M_{ij} = \delta_{i,1}a_j+\delta_{i,2}b_j+\delta_{i,3}c_j $$