To find the determinant of the 2x2 matrix:

\[
\begin{vmatrix}
3 & -1 \\
3 & 0 \\
\end{vmatrix}
\]

The formula for the determinant of a 2x2 matrix \(\begin{vmatrix} a & b \\ c & d \end{vmatrix}\) is:

\[
\text{Determinant} = (a \cdot d) - (b \cdot c)
\]

For your matrix:

\[
a = 3, \quad b = -1, \quad c = 3, \quad d = 0
\]

Substituting these values into the formula:

\[
\text{Determinant} = (3 \cdot 0) - (-1 \cdot 3) = 0 + 3 = 3
\]

So, the determinant is **3**.

Would you like further details or have any questions?

Here are 5 related questions you can explore:
1. How do you find the determinant of a 3x3 matrix?
2. What does the determinant of a matrix represent geometrically?
3. How do you know if a matrix is invertible using its determinant?
4. What are the properties of determinants in larger matrices?
5. How can determinants be used in solving systems of linear equations?

**Tip:** If the determinant of a matrix is 0, it means the matrix is singular and not invertible.

Learn how to calculate the determinant of a 2x2 matrix with the given values (3 -1) and (3 0). This step-by-step guide explains the determinant formula, key matrix concepts, and its applications. Ideal for students in Grades 9-12.

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