Determinant of 2 x 2 Matrix

det A = ad - bc

If the determinant of a matrix is not equal to zero, then the matrix has an inverse.

Solving for an unknown:

• det A = ad - bc

• -3x - 5 = 16

• -3x = 21

• x = -7

Determinants:

Area of a Triangle

• Area of Triangle is 1/2(bh). Given the vertices in the coordinate plane...

• x-coordinates in 1st column

• y-coordinates in 2nd column

• all 1's in 3rd column

• Find det of 3x3

• Area should always be positive, so multiply by 1/2 accordingly

Example: Find the area of a triangle whose vertices have the coordinates

(1, 2), (4, 0), and (6, 2)

see the next slide