Download Determinants

Find the Area of the following
Triangles
Determinants
Determinants
Associated with every square matrix
is a whole number called the
determinant
The Determinant of a Matrix A is
denoted by
detA or |A|
Determinant - a square array of
numbers or variables enclosed between
parallel vertical bars.
**To find a determinant you must have
a SQUARE MATRIX!!**
Finding a 2 x 2 determinant:
a b
= ad - bc
c d
Find the determinant:
5 7
1.
11 8
 58  711  40  77
40  77
3 2
2.
1 5
 37
 35  21  15  2
15  2

17
Expansion by Minors
a b
d e
g h
c
f
i
e
a
h
f
d
b
i
g
f
d e
c
i
g h
 same opp same
Always: 

opp
same
opp


 same opp same
Finding a 3x3 determinant: Expansion by Minors Method
2 7 3
6. Evaluate  1 5  4
6 9 0
5 4
1  4
1 5
2
7
 (3)
9 0
6 0
6 9
Step 1:
Expand the matrix
into 3 pieces.
Step 2:
Evaluate each
2x2 matrix.
Step 3:
Simplify.
2(0  (36))  7(0  (24))  3(9  30)
21
Finding a 3x3 determinant: Diagonal method
2
4. 6
4
3 8
7 1
5
9
Step 1: Rewrite first two
columns of the matrix.
-224 +10 +162 = -52
2 3 8 2 3
4. 6 7 1 6 7
4 5
9 4 5
Step 2: multiply
diagonals going up!
Step 2: multiply
diagonals going down!
-126 +12 +240 =126
126 - (-52)
126 + 52
= 178
Step 3: Bottom
minus top!
-18 +50 +6 = 38
Step 2: multiply
5 1 2 5 1
diagonals going up!
5. 2 3 5 2 3
3 2 3 3 2 Step 2: multiply
diagonals going down!
45 - 15 + 8 = 38
38 - 38
=0
Step 3: Bottom
minus top!
Do Now: Copy down this problem.
Find the area of a triangle
whose vertices are
located at (-1, 6), (2, 4),
(0, 0).