https://file.aiquickdraw.com/mathbot/file/1727365501720ws5xrohb.jpg

The determinants of the matrices are:

- For Question 5: The determinant is **-69**.
- For Question 6: The determinant is **-134.5**.

Let me know if you need more details or have any questions.

Here are 5 follow-up questions related to this topic:
1. How do you calculate the determinant of a 3x3 matrix?
2. What is the geometric interpretation of a matrix's determinant?
3. Can a matrix with a determinant of zero have an inverse?
4. What are the properties of determinants with respect to matrix multiplication?
5. How does changing a single element of a matrix affect its determinant?

**Tip:** A matrix's determinant can help determine if the system of linear equations it represents has a unique solution. If the determinant is zero, the system has no unique solution.

Identify the determinant of the matrices as shown in the image (one matrix with values [-3, 0, 7], [-2, 6, -1], [0, 3, 1] and another matrix with values [0.5, -6, 3.5], [0, 2, -4], [-8, 0, 1.5]).

This page provides a detailed explanation on how to find the determinant of two 3x3 matrices. The determinants for the matrices [-3, 0, 7], [-2, 6, -1], [0, 3, 1] and [0.5, -6, 3.5], [0, 2, -4], [-8, 0, 1.5] are calculated using the determinant formula for 3x3 matrices. Perfect for students learning linear algebra and matrix theory.

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