Multiple choice

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

  1. $\begin{vmatrix} 1& x(x+1) & x+1\\\\ 1& y(y+1) & y+1\\\\ 1& z(z+1) & z+1 \end{vmatrix}$
  2. $\begin{vmatrix} 1& x+1 & x^{2}+1\\\\ 1& y+1 & y^{2}+1\\\\ 1& z+1 & z^{2}+1 \end{vmatrix}$
  3. $\begin{vmatrix} 0& x-y & x^{2}-y^{2}\\\\ 0& y-z & y^{2}-z^{2}\\\\ 1& z & z^{2} \end{vmatrix} $
  4. $\begin{vmatrix} 2& x+y & x^{2}+y^{2}\\\\ 2& y+z & y^{2}+z^{2}\\\\ 1& z & z^{2} \end{vmatrix}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If matrix B is obtained from matrix A by replacing the lth row by itself plus k times the mth row for l $\sigma$ m, then det(2) = det(1). With this property, given matrix is equal to the matrices given in the options (2), (3) and (4).

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