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Determinant of 3x3 Matrix
R1C1
R = RowC = Column
3x3R2R3
C2 C3
A =a11
a21
a31
det(A)= | A | det =
Determinant(A) = of A
| A | = Matrix
R1C1
a12 a13
a32 a33
a22 a23
C2 C3
R3R2
a22
a32a11
x a23
a33
det(A)= | A | det =
Determinant(A) = of A
| A | = Matrix
A =a11
xx
R1C1
x x
a32 a33
a22 a23
C2 C3
R3R2
a21 a23
a31 a33a12
x
det(A)= | A | det =
Determinant(A) = of A
| A | = Matrix
A =xa21
a31
R1C1
a12 x
x a33
x a23
C2 C3
R3R2
a21 a22
a31 a32a13
x
det = Determinant(A) = of A
| A | = Matrix
A =xa21
a31
R1C1
x a13
a32 xa22 x
C2 C3
R3R2
det(A)= | A |
a22 a23
a32 a33+a11
xa21 a23
a31 a33-a12
xa21 a22
a31 a32+a13
x
Basic Formula
for Computin
gDetermin
ant
det = Determinant(A) = of A
| A | = Matrix
det(A)= | A |
+C1
Always Remember in
Matrix 1st is Positive & 2nd is Negative!
C2 C3- +
- + -+ - +
R2R1
R3
A =
1 6 42 7 38 9 5
Exampledet(A)= |
A |
A =
1 x xx 7 3x 9 5
det(A)=
7 39 5+
1x
Example
det(A)=x 6 x2 x 38 x 5
x 28
35-6
ExampleA =
det(A)=x x 42 7 x8 9 x
2 78 9+
4x
ExampleA =
det(A)=
7 39 5+
1x 2
835-6x
42 78 9
2 78 9+
4x
1 635
A =
Example
7 39 5+
1x 2
835-6x 2 7
8 9+4
x--Now; Do Cross Multiply--
1(7x5-9x3)-6(2x5+8x3)4(2x9+8x7)1(35-27)-6(10-24)4(18-56)
1(8)-6(-14)4(-38)8+84-152
92-152 = -60
