1. Let's start by understanding what a matrix and determinant are. 2. A matrix is a rectangular array of numbers arranged in rows and columns. 3. The determinant is a special number that can be calculated from a square matrix. 4. For a 2x2 matrix $ \begin{bmatrix} a & b \\ c & d \end{bmatrix} $, the determinant is calculated as: $$\det = ad - bc$$ 5. For a 3x3 matrix $ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} $, the determinant is: $$\det = a(ei - fh) - b(di - fg) + c(dh - eg)$$ 6. Important rules: - The determinant is only defined for square matrices. - If the determinant is zero, the matrix is singular (non-invertible). 7. Example: Calculate the determinant of $ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $ 8. Using the formula: $$\det = (1)(4) - (2)(3) = 4 - 6 = -2$$ 9. So, the determinant is $ -2 $. 10. This means the matrix is invertible since the determinant is not zero. This is a basic preparation for matrices and determinants.