Finding Determinants
Calculate determinants of 2×2 and 3×3 matrices in Grade 10 algebra using the formula ad-bc for 2×2 and cofactor expansion for 3×3, applying results to find area and solve systems.
Key Concepts
New Concept Every square matrix is associated with one real number called the determinant of the matrix.
What’s next Next, you’ll master the technique for calculating the determinant of $2 \times 2$ and $3 \times 3$ matrices and use it to solve problems.
Common Questions
How do you find the determinant of a 2×2 matrix [[a,b],[c,d]]?
det = ad - bc. For [[3,2],[1,4]]: det = 3(4) - 2(1) = 12 - 2 = 10.
What does a zero determinant mean?
A zero determinant means the matrix is singular (non-invertible). The corresponding system of equations has no unique solution — it is either inconsistent or dependent.
How is the determinant used to find the area of a parallelogram?
If vectors (a,b) and (c,d) form the sides of a parallelogram, the area equals |det [[a,b],[c,d]]| = |ad-bc|.