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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 andJacobsthal-Lucas numbers. Considering these sequences, we define the matrixsequences which have elements of $\{J_{n}^{(3)}\}_{n\in \mathbb{N}}$ and$\{j_{n}^{(3)}\}_{n\in \mathbb{N}}$. Then we investigate their properties.

On the third-order Jacobsthal and third-order Jacobsthal-Lucas sequences and their matrix representations