https://file.aiquickdraw.com/mathbot/file/17273136869755wu6n8t8.jpg

Let’s go through the questions from the image one by one.

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### **1. Diberikan Matriks \( A \) dan \( B \) dengan penjumlahan \( B + A = \begin{pmatrix} 16 & 8 \\ 1 & 2 \end{pmatrix} \). Tentukan matriks \( A \) dan \( B \)!**

- Matrix \( A = \begin{pmatrix} x - 2y & y \\ 4 & 1 \end{pmatrix} \)
- Matrix \( B = \begin{pmatrix} 5 & 3 \\ 2x & x - y \end{pmatrix} \)

The sum of matrices \( A \) and \( B \) is given as:

\[
B + A = \begin{pmatrix} 16 & 8 \\ 1 & 2 \end{pmatrix}
\]

We will equate the elements of matrices \( A \) and \( B \) to this sum to find \( x \), \( y \), and the values of the matrices.

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### **2. Tentukan hasil perkalian matriks \( \begin{pmatrix} 1 & 3 & 2 \\ 3 & 4 & 1 \\ 5 & 6 & 2 \end{pmatrix} \times \begin{pmatrix} 2 & 4 \\ 4 & 1 \\ 3 & 3 \end{pmatrix} \)!**

This is a matrix multiplication problem. We will multiply the \( 3 \times 3 \) matrix with the \( 3 \times 2 \) matrix.

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### **3. Berapakah nilai determinan dari matriks \( A = \begin{pmatrix} 50 & 75 & 40 \\ 30 & 45 & 25 \\ 32 & 50 & 30 \end{pmatrix} \)?**

We are tasked with calculating the determinant of the given \( 3 \times 3 \) matrix.

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### **4. Tentukan determinan dari matriks \( A = \begin{pmatrix} 3 & 1 \\ 2 & 5 \end{pmatrix} \)!**

This is a simple \( 2 \times 2 \) matrix determinant problem. The formula for a \( 2 \times 2 \) determinant is:

\[
\text{Determinant} = ad - bc
\]

where the matrix is \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \).

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### **5. Berapakah invers dari matriks \( A = \begin{pmatrix} 4 & 3 & 5 \\ 3 & 4 & 5 \\ 5 & 7 & 4 \end{pmatrix} \)!**

Here, we need to find the inverse of a \( 3 \times 3 \) matrix. The inverse of a matrix \( A \) is given by:

\[
A^{-1} = \frac{1}{\det(A)} \text{adj}(A)
\]

where \( \det(A) \) is the determinant of the matrix and \( \text{adj}(A) \) is the adjugate of the matrix.

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Let me start by solving these problems step by step. I'll calculate the solutions now.It seems like there was an issue with extracting the values for \( x \) and \( y \) from the solution of the equations. Let me adjust the process to properly retrieve and solve for these variables.

I'll fix the calculations and proceed with solving the rest of the problems correctly.It seems like the system didn't return multiple solutions in the expected format. Let me refine the process to extract the values of \( x \) and \( y \) correctly and then continue solving the matrix problems.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through these calculations manually? Let me know if you have any specific questions!

Here are 5 related questions that may help expand your understanding:
1. How do you find the solution of a system of linear equations involving two variables?
2. What is the method for performing matrix multiplication?
3. How do you calculate the determinant of a 3x3 matrix using cofactor expansion?
4. Why is the determinant important in calculating a matrix's inverse?
5. What are the conditions for a matrix to have an inverse?

**Tip:** Always double-check your matrix operations, especially for addition, multiplication, and determinant calculations, as small mistakes can lead to incorrect results.

1. Diberikan matriks A dan B dengan penjumlahan B + A = [[16, 8], [1, 2]]. Tentukan matriks A dan B!
2. Tentukan hasil perkalian matriks [[1, 3, 2], [3, 4, 1], [5, 6, 2]] x [[2, 4], [4, 1], [3, 3]]!
3. Berapakah nilai determinan dari matriks A = [[50, 75, 40], [30, 45, 25], [32, 50, 30]]?
4. Tentukan determinan dari matriks A = [[3, 1], [2, 5]]!
5. Berapakah invers dari matriks A = [[4, 3, 5], [3, 4, 5], [5, 7, 4]]!

Solve problems involving matrix addition, multiplication, determinants, and inverses. This includes finding matrices A and B, calculating matrix products, determinants, and inverses. Suitable for high school students in Grades 10-12.

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