Determinant of a 2x2 matrix $M$ is calculated using the formula:

$\text{det}(M) = (ad - bc)$

Given matrix $M = \begin{bmatrix} 6 & 3 \\ 7 & 4 \end{bmatrix}$, where:

• $a = 6$
• $b = 3$
• $c = 7$
• $d = 4$

Now, applying the formula:

$\text{det}(M) = (6 \times 4) - (3 \times 7) = 24 - 21 = 3$

So, the determinant of matrix $M$ is 3.

Would you like further details on determinants, or do you have any questions?

Here are 5 related questions to expand on this topic:

1. How is the determinant useful in solving systems of equations?
2. What happens if the determinant of a matrix is zero?
3. Can you calculate the determinant for a 3x3 matrix?
4. What are properties of determinants for larger matrices?
5. How does the determinant relate to the inverse of a matrix?

Tip: A matrix is invertible only if its determinant is non-zero!