determinant of matrix

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