A matrix is a rank 2 tensor i.e. an array expanding in a maximum of two independent dimensions. Multiple vectors could be arranged in rows or columns to create a matrix. $$\vec{a} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}\ \ \vec{b} = \begin{bmatrix} 7 \\ 9 \\ 10 \end{bmatrix}$$ $$\textbf{A} = \begin{bmatrix} \vec{a} & \vec{b} \end{bmatrix} = \begin{bmatrix} 5 & 7 \\ 6 & 9 \\ 7 & 10 \end{bmatrix}$$...
A vector could represent the magnitude of a quantity broken down into its various components, for example, the velocity of an object moving on a 2D plane could be represented using the vector $\vec{v} = \begin{bmatrix} 8 & 9 \end{bmatrix}$. On a 2D plane $8$ and $9$ could be called the horizontal and vertical components of the vector $\vec{v}$ respectively. But the words horizontal and vertical on a 2D or 3D plane are relative to the viewer (try rotating the figure above anti-clockwise)....
In linear algebra, a tensor is an array of data expanding in multiple (or zero) independent dimensions. It is used to represent quantities/equations/functions with multiple components, for example, the equation $3x+2y=0$ could be represented with the tensor $[3\ 2\ 0]$ where each value in the tensor represents the different components of the equation. The number of independent dimensions of a tensor is called its rank. Vectors and matrices could be generalized with the term tensor....