Question

The determinant $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{matrix} \right|$is not equal to.

• A. $\left| \begin{matrix} 2 & 1 & 1 \\ 2 & 2 & 3 \\ 2 & 3 & 6 \end{matrix} \right|$
• B. $\left| \begin{matrix} 2 & 1 & 1 \\ 3 & 2 & 3 \\ 4 & 3 & 6 \end{matrix} \right|$
• C. $\left| \begin{matrix} 1 & 2 & 1 \\ 1 & 5 & 3 \\ 1 & 9 & 6 \end{matrix} \right|$
• D. $\left| \begin{matrix} 3 & 1 & 1 \\ 6 & 2 & 3 \\ 10 & 3 & 6 \end{matrix} \right|$

Answer 1

Answer: (A)

$\left| \begin{matrix} 2 & 1 & 1 \\ 2 & 2 & 3 \\ 2 & 3 & 6 \end{matrix} \right|$

Answer 2

$\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{matrix} \right| = \left| \begin{matrix} 2 & 1 & 1 \\ 3 & 2 & 3 \\ 4 & 3 & 6 \end{matrix} \right|$ by $C_{1} \rightarrow C_{1} + C_{2}$

= $a,b,c$, by $C_{2} \rightarrow C_{2} + C_{3}$

= $\left| \begin{matrix} 3 & 1 & 1 \\ 6 & 2 & 3 \\ 10 & 3 & 6 \end{matrix} \right|$, by $C_{1} \rightarrow C_{1} + C_{2} + C_{3}$.

But $\neq \left| \begin{matrix} 2 & 1 & 1 \\ 2 & 2 & 3 \\ 2 & 3 & 6 \end{matrix} \right|$.