37 Determinants Determinants Standard What is a determinant and how is it used Essential Question A4b Find the inverses of two by two matrices Associated with every square matrix is a whole number called the ID: 382644
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Slide1
Table of Contents
37
. DeterminantsSlide2
Determinants
Standard
What is a determinant and how is it used?
Essential Question
A4b Find the inverses of two by two matricesSlide3
Associated with every
square
matrix is a whole number called the determinant
The determinant of a Matrix A is denoted by detA or
|A|VOCABULARYSlide4
=
ad
-
cb
How to find a determinant of 2x2Slide5
Ex. 1. Evaluate the determinant
=
1(7)
-
4(2)
= 7 - 8
= -1Slide6
Find the determinant
=7(3)
- 2(2)
= 21 - 4
= 17Slide7
Step 1: recopy the first two columns.
Step 2: multiply down the diagonals and add the products
Step 3: multiply up diagonals and add the products
Step 4: Subtract the up diagonal from the down diagonal
(down – up)
Steps for finding determinant of a 3 x 3 matrixSlide8
Ex. 2 Evaluate
= -73
Step 1: recopy the first two columns.
-3
-2 0
1 2
=
(
2*0*6
+
-3*3*1
+
4*-2*2)
_
(1*0*4
+
2*3*2
+ 6*-2*-3)
= (0 + -9 + -16) – (0 + 12 + 36)
= -25 - 48
Step 2: multiply the
down diagonals and
add the products.
Step 3: multiply the
up diagonals and
add the products
NOTE: You
subtract
the up diagonal from the down diagonalSlide9
You try!!!
= -89
detSlide10
Area of a Triangle!
The area of a triangle with vertices (x
1,y
1), (x2,y2), and (x3
,y3)Area =
*Where
± is used to produce a positive area!!Slide11
Ex. 3 Find the area of the triangle.
Area=Slide12
You try!! Find the area of the triangle.
Area=Slide13
Homework
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