GATE CSE 2013 | Question: 3

Question

Which one of the following does NOT equal $$\begin{vmatrix} 1 & x & x^{2}\\ 1& y & y^{2}\\ 1 & z & z^{2} \end{vmatrix} \quad ?$$

• A. $\begin{vmatrix} 1& x(x+1)& x+1\\ 1& y(y+1) & y+1\\ 1& z(z+1) & z+1 \end{vmatrix}$
• B. $\begin{vmatrix} 1& x+1 & x^{2}+1\\ 1& y+1 & y^{2}+1\\ 1& z+1 & z^{2}+1 \end{vmatrix}$
• C. $\begin{vmatrix} 0& x-y & x^{2}-y^{2}\\ 0 & y-z & y^{2}-z^{2}\\ 1 & z & z^{2} \end{vmatrix}$
• D. $\begin{vmatrix} 2& x+y & x^{2}+y^{2}\\ 2 & y+z & y^{2}+z^{2}\\ 1 & z & z^{2} \end{vmatrix}$

Comments

Yes, try to substitute different $-$different values and eliminate the options.

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What is a,b and c here?

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see above comment $a,b,c$ is nothing but $x,y,z$

Answer 1

https://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant    ( properties of Determinant 

https://en.m.wikipedia.org/wiki/Determinant#Immediate_consequences  ( 2nd applied )

Answer 2

A is the Answer