Question 1119679
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My doubt is show that in matrix [1 a a^2-bc]
                                                         [1 b b^2-ac]    = 0.
                                                         [1 c c^2-ab]
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Based on your post,  I only can guess what do you need.


If you need to calculate the determinant,  apply co-factoring the determinant along the first column.


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> 

in this site, &nbsp;where co-factoring along the first row was described.


Co-factoring along the first column works in the same way.