1. The problem is to understand the given 2x3 matrix: $$\begin{bmatrix} 12x^3 - 2 & 4 \\ 6x - 5 & 2 \end{bmatrix}$$ 2. This matrix has 2 rows and 2 columns (not 3 columns as stated), with elements: - First row: $12x^3 - 2$, $4$ - Second row: $6x - 5$, $2$ 3. Since the problem only shows the matrix, we can analyze or simplify its elements if needed. 4. For example, we can factor or simplify each element: - $12x^3 - 2 = 2(6x^3 - 1)$ - $4$ is already simplified. - $6x - 5$ is linear and cannot be factored further. - $2$ is a constant. 5. If the goal is to perform operations like finding the determinant, note that determinant is defined only for square matrices. This is a 2x2 matrix, so determinant can be calculated: $$\text{det} = (12x^3 - 2)(2) - (4)(6x - 5)$$ 6. Calculate the determinant step-by-step: $$= 2(12x^3 - 2) - 4(6x - 5)$$ $$= 24x^3 - 4 - 24x + 20$$ 7. Combine like terms: $$= 24x^3 - 24x + 16$$ 8. Final answer: The determinant of the matrix is $$24x^3 - 24x + 16$$.