Question

The value of $\left|\begin{array}{ccc}a& a+b& a+b+c\\ 2a& 3a+2b& 4a+3b+2c\\ 3a& 6a+3b& 10a+6b+3c\end{array}\right|$ is equal to

• A. $a^3$
• B. $b^3$
• C. $c^3$
• D. $a^3+b^3+c^3$

Answer 1

The correct option is A $a^3$

Use $R_2\to R_2-2R_1$ and $R_3\to R_3-3R_1$

$\Rightarrow \left|\begin{array}{ccc}a& a+b& a+b+c\\ 0& a& 2a+b\\ 0& 3a& 7a+3b\end{array}\right|$

$R_3\to R_3-3R_2$

$\Rightarrow \left|\begin{array}{ccc}a& a+b& a+b+c\\ 0& a& 2a+b\\ 0& 0& a\end{array}\right|=a^3$