https://file.aiquickdraw.com/mathbot/file/1726718230360tn2b44vn.jpg

The problem in the image asks for the determinant of the matrix:

\[
\begin{pmatrix} 
1 & 2 \\ 
3 & 4 
\end{pmatrix}
\]

The determinant of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) is calculated as:

\[
\text{determinant} = (a \times d) - (b \times c)
\]

Substituting the values from the given matrix:

\[
\text{determinant} = (1 \times 4) - (2 \times 3) = 4 - 6 = -2
\]

Thus, the determinant is \(-2\), which corresponds to option **B**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you calculate the determinant of a 3x3 matrix?
2. What is the significance of the determinant of a matrix?
3. Can a matrix with a zero determinant be inverted?
4. What are the properties of matrix determinants?
5. How does the determinant change if you swap two rows of a matrix?

**Tip**: For larger matrices, cofactor expansion is used to compute determinants.

Determinant of the matrix [1 2; 3 4] is ...

Learn how to calculate the determinant of a 2x2 matrix [1 2; 3 4]. This problem highlights core concepts of determinants and matrix operations. Suitable for high school students (Grade 10-12).

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