Determinants of Matrices

Determinants of Matrices

2x2 and 3x3 matrices

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.

Fill in the Blanks

Find the determinant of matrix B.

 

Fill in the Blanks

Given the matrix, find the determinant.

Multiple Choice

Find the determinant of the matrix and determine of the matrix is invertible.

• det = -14, inverse exists

• det = 0, no inverse exists

• det = 166, inverse exists

• det = 14, inverse exists

Multiple Choice

Find the value of x that makes the equation true.

• x = 7

• x = -11/3

• x = 19

• x = -7

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

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

Fill in the Blanks

Find the area of triangle ELI where E=(2, 11), L=(7, 1) and I=(2, 1)

Fill in the Blanks

Find the area of the triangle in the figure. Use decimal if necessary.

Multiple Choice

Donovan was using determinants to find the area of a triangle. She calculated the area to be zero. What conclusion can she make?

• There was a math mistake. It is impossible for det A = 0

• The area of the triangle is zero.

• If det A = 0, then the 3 points are collinear, and no triangle is formed.

• She can't find the area of a triangle using determinants because the matrix isn't square.

Multiple Choice

Find the exact area of the following triangle whose vertices have the given coordinates. (-4, -1), (3, 2), and (4, 6)

• Area = 27

• Area = 14

• Area = 52

• None of these

Fill in the Blanks

Find the exact area of the following triangle whose vertices have the given coordinates. (4, -5), (3, -8), and (-1, 3) Use decimal if necessary.

Fill in the Blanks

Find the exact area of the following triangle whose vertices have the given coordinates. (-2, 2), (1, 3), and (3, 0). Use decimal if necessary.