Matrix, Find determinant using properties of Det.

[am_knightmare]

Homework Statement

1 1 1
a b c = (b-a)(c-a)(c-b)
a^2 b^2 c^2
(above is a 3x3 matrix equaling to a equation)
question:"Show by applying property of the determinant"

Homework Equations

N/A

The Attempt at a Solution

read through the whole chapter of determinants, there were no similar problems. read it the second time focusing on properties, no simimlar properties, Please help.

 

[Dick]

Start by subtracting the first column from the second and third columns. Then think about an expansion by minors.

 

[am_knightmare]

Just solved it. thanks for the reply though.
1 1 1
a b c
a^2 b^2 c^2
becomes
1 0 0
a b-a c-a
a^2 (b^2-a^2) (c^2-a^2)
then becomes
(b-a)(c-a) times
1 0 0
a 1 1
a^2 b-a c-a
then
1 0 0
a 1 0
a^2 b-a c-b
det= 1 x 1 x(c-b) ( c-a) (b-a)

 

[Dick]

Just solved it. thanks for the reply though.
1 1 1
a b c
a^2 b^2 c^2
becomes
1 0 0
a b-a c-a
a^2 (b^2-a^2) (c^2-a^2)
then becomes
(b-a)(c-a) times
1 0 0
a 1 1
a^2 b-a c-a
then
1 0 0
a 1 0
a^2 b-a c-b
det= 1 x 1 x(c-b) ( c-a) (b-a)

Yup. That'll do it.