https://file.aiquickdraw.com/mathbot/file/1728354812180401yd8qc.jpg

The image asks to calculate the determinant of the following matrix:

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

The determinant of a 2x2 matrix 

\[
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\]

is given by the formula:

\[
\text{det}(A) = ad - bc
\]

For the given matrix:

\[
\text{det}\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} = (1)(4) - (2)(3) = 4 - 6 = -2
\]

Thus, the determinant of the matrix is **-2**.

Would you like more details on how matrix determinants work?

Here are some related questions:
1. How do you compute the determinant of a 3x3 matrix?
2. What properties of a matrix can be derived from its determinant?
3. Can a matrix with a determinant of zero be inverted?
4. How is the determinant used in solving systems of linear equations?
5. How do eigenvalues relate to the determinant of a matrix?

**Tip:** For a square matrix of any size, a zero determinant indicates that the matrix is singular and cannot be inverted.

Calculate the determinant of the following 2x2 matrix:
\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}

Learn how to calculate the determinant of the matrix \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}. This detailed solution walks through key linear algebra concepts, including the determinant formula for a 2x2 matrix: det(A) = ad - bc. Suitable for Grades 9-12.

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