https://file.aiquickdraw.com/mathbot/file/1726542796664xonl669a.jpg

Let's solve the given matrix problem step by step.

The equation shown is:

\[
\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} - \begin{pmatrix} 7 & 8 \\ 4 & 6 \end{pmatrix}
\]

First, we need to subtract the two matrices:

\[
\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} - \begin{pmatrix} 7 & 8 \\ 4 & 6 \end{pmatrix} = \begin{pmatrix} 3 - 7 & 2 - 8 \\ 1 - 4 & 4 - 6 \end{pmatrix}
\]

This simplifies to:

\[
\begin{pmatrix} -4 & -6 \\ -3 & -2 \end{pmatrix}
\]

Next, we calculate the determinant of the resulting matrix:

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

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

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

For the matrix \(\begin{pmatrix} -4 & -6 \\ -3 & -2 \end{pmatrix}\):

\[
\text{det}(A) = (-4)(-2) - (-6)(-3) = 8 - 18 = -10
\]

Thus, the determinant of matrix \(A\) is \(-10\).

The correct answer is option **A: -10**.

Would you like any additional explanation or details?

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Here are 5 related questions to deepen your understanding:

1. How do you calculate the determinant of a 3x3 matrix?
2. What happens to the determinant if you switch two rows of a matrix?
3. How is matrix subtraction defined for matrices of different sizes?
4. What is the geometrical meaning of the determinant of a matrix?
5. Can a matrix with a determinant of 0 have an inverse?

**Tip:** The determinant can help determine whether a matrix is invertible—if the determinant is 0, the matrix is singular and has no inverse!

Jika matriks A memenuhi (3 2 1 4) - (7 8 4 6), maka det(A) = ?

Learn how to subtract two 2x2 matrices and calculate the determinant of the resulting matrix. This example uses matrix subtraction followed by the determinant formula. Suitable for students in Grades 10-12.

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