https://file.aiquickdraw.com/mathbot/file/1726582433005kwrsnlda.jpg

Let's break down the problems presented in the image:

1) **Invers of matrices**:
   - The task is to find the inverse of two matrices \( A \) and \( B \):
     - Matrix \( A = \begin{bmatrix} 2 & 1 \\ 1 & -3 \end{bmatrix} \)
     - Matrix \( B = \begin{bmatrix} 1 & 1 & -6 \\ 1 & -3 & 0 \\ 0 & 2 & 4 \end{bmatrix} \)

2) **Solve systems of equations**:
   - a) \( \begin{cases} 2x + 3y = 8 \\ 3x + y = 5 \end{cases} \)
   - b) \( \begin{cases} 4x + y = 9 \\ x + 4y = 6 \end{cases} \)
   - c) \( \begin{cases} 2x + y + 2z = 4 \\ -x - y + z = 5 \\ 2x + 2y + z = -1 \end{cases} \)

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I will proceed by calculating the inverse of matrices \( A \) and \( B \) and solving the systems of equations step by step.

Let me start with matrix \( A \) and \( B \)'s inverses and the solutions to the equation systems.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can explain how to calculate the inverse of a matrix and solve systems of equations step-by-step manually, or you can provide a different question.

Here are five follow-up questions based on the content we discussed:
1. How do you find the determinant of a 2x2 matrix?
2. What happens if a matrix is singular? Can it still have an inverse?
3. How do you solve a system of linear equations using the substitution method?
4. Can you apply Gaussian elimination to solve systems of equations with three variables?
5. How does matrix multiplication work when solving systems of linear equations?

**Tip**: When solving for the inverse of a matrix, always check if the determinant is non-zero first; if it's zero, the matrix does not have an inverse!

1) Find the inverse of matrices A and B. 2) Solve the system of equations in parts a, b, and c.

Learn how to find the inverse of matrices A and B and solve systems of linear equations using Gaussian elimination and Cramer's rule. This problem covers matrix algebra and solving simultaneous equations. Suitable for students in Grades 10-12.

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