Lesson 12: Determinants of a Matrix

Determinants of a Matrix

I'm out of Matrix puns...

​Finding the Determinant of a 2x2 Matrix

​To find the determinant of matrices, we draw diagonals through the terms. In a 2x2 matrix, we draw two diagonals: one going down through a and d and one going up through c and b. We multiply the terms in each diagonal and then subtract the upward diagonal product from the downward diagonal product.

​Finding the Determinant of a 3x3 Matrix

In a 3x3 matrix, we still draw our diagonals. This time, we write the first two columns of the matrix to the right of the matrix. Then, we draw 6 diagonals, one through each term in the first row of the matrix going downward and one through each term in the third row of the matrix going up. Then, we subtract the upward product from the downward product.

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​Finding the Area of a Triangle Using Determinants

​We can use the determinant of a 3x3 matrix to solve the area of a triangle in a Cartesian plane given just the coordinates of the vertices of the triangle. The formula is shown to the right where x₁ and y₁ is the coordinate pair of one vertex, x₂ and y₂ are another vertex and x₃ and y₃ are the last vertex. Area is always positive.

Multiple Choice

Find the area of a triangle whose vertices are A (2, 3), B (3, 2) and C (1, 8).

• - 15

• 15

• 10

• none of these

Multiple Choice

A triangle has vertices as (1, 2), (3, –4), and (–2, 3). Find the area of the triangle.

• Area = 16

• Area = 8

• Area = 32

• None of these