The "discriminant" is a concept generally used in relation to polynomials and quadratic equations, rather than directly to matrices. However, based on your question, I believe you're referring to the determinant of a 3x3 matrix, which is a common measure of a matrix's properties. The determinant provides information about a matrix, including whether it is invertible and the volume scaling factor of the linear transformation it represents.

For a 3x3 matrix with entries ranging from -10 to 10, the maximum possible value of the determinant can be calculated by considering the matrix with entries that maximize the determinant formula.

The determinant $\text{det}(A)$ of a 3x3 matrix $A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}$ is given by:

$\text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$

To maximize the determinant, we need to select values that maximize each term. Setting the entries to the extreme values of the range $[-10, 10]$ is a way to approach this. Using $\pm 10$ for the matrix elements can result in a maximum value.

For example, consider this matrix:

$A = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 10 \end{pmatrix}$

The determinant of this matrix is:

$\text{det}(A) = 10 \times (10 \times 10 - 0 \times 0) - 0 \times (0 \times 10 - 0 \times 0) + 0 \times (0 \times 0 - 10 \times 0)$ $\text{det}(A) = 10 \times (100) = 1000$

Thus, the maximum possible determinant of a 3x3 matrix with entries ranging from -10 to 10 is $\boxed{1000}$.

Would you like more details about matrix determinants or the properties they reveal? Here are five related questions to deepen the understanding:

1. How does the determinant of a matrix relate to its invertibility?
2. What is the geometric interpretation of the determinant in 2D and 3D?
3. How does the sign of the determinant affect the properties of a matrix?
4. What happens to the determinant if you swap rows or columns of a matrix?
5. Can the determinant be used to solve systems of linear equations using Cramer's Rule?

Tip: The determinant of a matrix changes sign if you swap two rows or two columns.