An educational infographic on Determinants in Mathematics featuring: Key Concepts: Definition of determinants for 2x2 and 3x3 matrices with formulas Visual Calculations: Step-by-step expansion of determinants using Sarrus' Rule (for 3x3) Applications: Solving systems of equations (Cramer's Rule), area of triangles using coordinates, and physics/engineering uses.

Determinants

1. Calculate the determinant of the 2×2 matrix:
– ( begin{vmatrix} 1 & 2 \\ 3 & 4 end{vmatrix} )
2. Find the determinant of the 2×2 matrix:
– \( begin{vmatrix} 5 & -3 \\ 2 & 6 end{vmatrix} \)
3. Determine the determinant of the 3×3 matrix:
– \( begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 end{vmatrix} \)
4. Compute the determinant of the 3×3 matrix:
– \( begin{vmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 end{vmatrix} \)
5. Calculate the determinant of the 3×3 matrix:
– \( begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 1 & 0 & 0 end{vmatrix} \)
6. Determine the determinant of the 2×2 matrix:
– \( begin{vmatrix} 4 & 7 \\ 2 & 6 end{vmatrix} \)
7. Compute the determinant of the 3×3 matrix:
– \( begin{vmatrix} 2 & 0 & 1 \\ 3 & 0 & 2 \\ 1 & 1 & 1 end{vmatrix} \)
8. Find the determinant of the 3×3 matrix:
– \( begin{vmatrix} -2 & 3 & 5 \\ 1 & -2 & 1 \\ 3 & 4 & -1 end{vmatrix} \)
9. Determine the determinant of the 2×2 matrix:
– \( begin{vmatrix} 0 & 1 \\ -1 & 0 end{vmatrix} \)
10. Compute the determinant of the 3×3 matrix:
– \( begin{vmatrix} 1 & 2 & -1 \\ -2 & -3 & 1 \\ 3 & 5 & 0 end{vmatrix} \)
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