SOLUTION: Without expanding the determinant show that it is equal to 0. The elements in following determinant 1/a a^2 bc 1/b b^2 ca 1/c c^2 ab

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Question 1136420: Without expanding the determinant show that it is equal to 0.
The elements in following determinant
1/a a^2 bc
1/b b^2 ca
1/c c^2 ab
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
Multiply the left column of the given matrix by the factor (a*b*c).


You will get exactly the right column of the given matrix.


Now use this property of the determinant:


    determinant of a matrix is zero, if one its column is proportional to another.

Answered, solved and completed.