  In this paper, we first give new generalizations for third-order Jacobsthal
$\{J_{n}^{(3)}\}_{n\in \mathbb{N}}$ and third-order Jacobsthal-Lucas
$\{j_{n}^{(3)}\}_{n\in \mathbb{N}}$ sequences for Jacobsthal and
Jacobsthal-Lucas numbers. Considering these sequences, we define the matrix
sequences which have elements of $\{J_{n}^{(3)}\}_{n\in \mathbb{N}}$ and
$\{j_{n}^{(3)}\}_{n\in \mathbb{N}}$. Then we investigate their properties.
