1. **State the problem:** We need to find the matrix $A$ given by the equation: $$A = 3.1 \begin{bmatrix} 1 & -4 & 0 \\ -2 & 2 & -1 \end{bmatrix} - 1.2 \begin{bmatrix} -1 & 2 & 5 \\ -2 & 0 & -3 \end{bmatrix}$$ and determine which of the given options matches the result. 2. **Recall the matrix scalar multiplication and subtraction rules:** - Multiply each element of a matrix by the scalar. - Subtract corresponding elements of the two matrices. 3. **Calculate each scalar multiplication:** $$3.1 \times \begin{bmatrix} 1 & -4 & 0 \\ -2 & 2 & -1 \end{bmatrix} = \begin{bmatrix} 3.1 & -12.4 & 0 \\ -6.2 & 6.2 & -3.1 \end{bmatrix}$$ $$1.2 \times \begin{bmatrix} -1 & 2 & 5 \\ -2 & 0 & -3 \end{bmatrix} = \begin{bmatrix} -1.2 & 2.4 & 6 \\ -2.4 & 0 & -3.6 \end{bmatrix}$$ 4. **Perform the subtraction:** $$A = \begin{bmatrix} 3.1 & -12.4 & 0 \\ -6.2 & 6.2 & -3.1 \end{bmatrix} - \begin{bmatrix} -1.2 & 2.4 & 6 \\ -2.4 & 0 & -3.6 \end{bmatrix} = \begin{bmatrix} 3.1 - (-1.2) & -12.4 - 2.4 & 0 - 6 \\ -6.2 - (-2.4) & 6.2 - 0 & -3.1 - (-3.6) \end{bmatrix}$$ 5. **Simplify each element:** $$A = \begin{bmatrix} 3.1 + 1.2 & -12.4 - 2.4 & 0 - 6 \\ -6.2 + 2.4 & 6.2 & -3.1 + 3.6 \end{bmatrix} = \begin{bmatrix} 4.3 & -14.8 & -6 \\ -3.8 & 6.2 & 0.5 \end{bmatrix}$$ 6. **Compare with the options:** The matrix matches the second option: $$\begin{bmatrix} 4.3 & -14.8 & -6 \\ -3.8 & 6.2 & 0.5 \end{bmatrix}$$ **Final answer:** $$A = \begin{bmatrix} 4.3 & -14.8 & -6 \\ -3.8 & 6.2 & 0.5 \end{bmatrix}$$