determinant

[bhuvaneshnick]

1. Prove, without expanding, that \(\displaystyle \left| \begin{array}{ccc}1&a&a^2\, -\, bc\\1&b&b^2\, -\, ca\\1&c&c^2\, -\, ab \end{array}\right|\) vanishes.

Without expanding how it vanishes,i mean what basic determinant property we have to apply to make it zero.Thank you

 

[Ishuda]

1. Prove, without expanding, that \(\displaystyle \left| \begin{array}{ccc}1&a&a^2\, -\, bc\\1&b&b^2\, -\, ca\\1&c&c^2\, -\, ab \end{array}\right|\) vanishes.

Without expanding how it vanishes,i mean what basic determinant property we have to apply to make it zero.Thank you

Probably row reduction. A nice discussion with a couple of examples is given at
http://thejuniverse.org/PUBLIC/Line...it.3/Presentation.1/Section3A/rowColCalc.html

Note that since you are told the determinate is zero, you really don't have to keep track of the sign changes, etc. but it is good practice to do so.