The image appears to be asking to express a matrix with some additional information. I'll extract the content and provide a clear interpretation and solution.

The visible part of the image reads:

"Nyatakanlah matriks $A = (a_{ij})$, di mana $A$ dan $P$ adalah matriks berikut, dan $B$ adalah determinan matriks-matriks berikut."

The matrix provided is:

1 & 3 & 4 \\ 2 & 5 & 7 \\ 4 & 2 & 7 \end{pmatrix}$$ The task asks to express the matrix $$A$$, determine if matrix $$P$$ is also involved, and calculate the determinant $$B$$. ### Let's solve: #### Step 1: Express matrix $$A$$. The matrix $$A$$ is already given: $$A = \begin{pmatrix} 1 & 3 & 4 \\ 2 & 5 & 7 \\ 4 & 2 & 7 \end{pmatrix}$$ #### Step 2: Calculate the determinant of matrix $$A$$. The determinant $$\text{det}(A)$$ can be computed using cofactor expansion or any preferred method for 3x3 matrices. I'll calculate that now. $$\text{det}(A) = 1 \times \begin{vmatrix} 5 & 7 \\ 2 & 7 \end{vmatrix} - 3 \times \begin{vmatrix} 2 & 7 \\ 4 & 7 \end{vmatrix} + 4 \times \begin{vmatrix} 2 & 5 \\ 4 & 2 \end{vmatrix}$$ Let me compute the result:import numpy as np # Define matrix A A = np.array([[1, 3, 4], [2, 5, 7], [4, 2, 7]]) # Calculate the determinant of A det_A = np.linalg.det(A) det_AThe determinant of matrix $$A$$ is $$\text{det}(A) = -1$$. ### Summary: 1. The matrix $$A$$ is given as: $$A = \begin{pmatrix} 1 & 3 & 4 \\ 2 & 5 & 7 \\ 4 & 2 & 7 \end{pmatrix}$$ 2. The determinant of matrix $$A$$, denoted as $$B$$, is $$-1$$. Would you like further details or clarification on any part? Here are a few related questions to explore: 1. How can you calculate the inverse of a matrix using the determinant? 2. What is the cofactor expansion method for calculating determinants? 3. How does the determinant help determine if a matrix is invertible? 4. What properties of matrices remain unchanged under determinant transformations? 5. Can we apply the same method for higher-dimensional matrices? **Tip**: A matrix is invertible if and only if its determinant is non-zero.