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

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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

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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