Geometric Application of Matrix Determinant and Transpose on Spheres and Cones

This example demonstrates how matrix operations (determinant and transpose) can be used to construct geometric objects such as spheres and cones in 3D space, illustrating the connection between linear algebra and geometry. Core mathematical concepts include the determinant and transpose of matrices, and their roles in geometric transformations (like scaling and rotation) and in representing geometric bodies. Construction highlights: using GeoGebra commands Determinant and Transpose, multiple matrix objects (matrix1, matrix2, matrix3) and point objects (A1, B1, A2, B2, A4, B4, C4, A5, B5, C5) are created, with the determinant d1 and transpose t1 driving the geometric construction. Suitable for high school or university courses in linear algebra and analytic geometry, this example helps students intuitively grasp the geometric meaning of matrix operations, and can serve as an introductory resource for mathematical modeling or computer graphics.