Finding Determinants
Lesson #14: p. 93-96
Warm-up Problems
1. A(n) _____________ (element, matrix) is
a rectangular array of numbers.
2. Solve 4x + 6 = 22
3. Simplify:
New Concepts
• Every square matrix is associated with
one real number called the determinant
of the matrix.
• If a matrix is not a square matrix, then it
does not have a determinant.
What is a determinant?
• The determinant of a square matrix is a
number that is uniquely associated with it.
• Each square matrix has exactly one
determinant.
• The determinant of a 2 x 2 square matrix is
found by subtracting the product of the
entries in one diagonal from the product of
the entries in the other diagonal.
Notation Distinction
• Recall the notation used to denote matrices:
square brackets.
• Enclosing a square matrix within vertical lines
designates the determinant of a matrix.
• The determinant of a 2 x 2 square matrix is
found by subtracting the product of the entries
in one diagonal from the product of the entries
in the other diagonal.
• Find the determinant of the following
matrix based on the definition.
Formula for finding the determinant
of a 2 x 2 matrix.
• The formula for the determinant of
the 2 x 2 matrix shown below is:
• ad – cb
Ex. 1 Finding the Determinant of a
2 x 2 Matrix
• Evaluate:
Solving Determinant Equations
• Solve for x.
Show your reasoning.
Finding the Determinant of a
3x3 Matrix
• Finding the determinant of a 3 x 3 matrix is
more involved than a 2 x 2 matrix.
• One strategy is called Expansion by Minors.
Determinant of a 3 x 3 Matrix:
Expansion by Minors
• This strategy involves choosing an element in the
first row, covering its row and column, and finding
the determinant of the remaining 2 x 2 matrix.
• The formula is given below.
Find the Determinant of the 3 x 3 matrix
using Expansion by Minors.
Find the Determinant of the 3 x 3 matrix
using Expansion by Minors.
Using a Graphing Calculator
to find the Determinant
1. Enter in the 3 x 3 matrix.
2. On the matrix Calc menu, choose “Det”
Using a Graphing Calculator
to find the Determinant
1. Enter in the 3 x 3 matrix.
2. On the matrix Calc menu, choose “Det”
Application: Geometry
• A triangle with vertices (x , y ), (x , y ), and
1
1
2
2
(x3, y3) has an area equal to the absolute
value of
Find the area of the triangle shown.
A triangle with vertices (x1, y1), (x2, y2),
and (x3, y3) has an area equal to the
absolute value of:
Partner Practice
• p. 97 Lesson Practice Problems a, b, c, ... f
• Summarizer: 2 Question Quiz
p. 98 #12 & 14
Individual Practice
• p. 98-99 #4, 6, 8, 10, 18, 20, 26, 28