First slide

Introduction to Determinants

Question

If $|\begin{array}{lll} x^{n} x^{n + 2} x^{n + 3} \\ y^{n} y^{n + 2} y^{n + 3} \\ z^{n} z^{n + 2} z^{n + 3} \end{array}|$ $= (x - y) (y - z) (z - x) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})$ , then n equals

Moderate

A

1
B

-1
C

2
D

-2

Solution

The degree of each term of the determinant is n + (n + 2) + (n + 3) = 3n + 5 and the degree of each term of the expression on R.H.S. is 2.
$∴ 3 n + 5 = 2 or n = - 1$

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