Question

The value of the determinant $\left|\begin{array}{ccc}a& a+2b& a+4b\\ a+2b& a+4b& a+6b\\ a+4b& a+6b& a+8b\end{array}\right|$ is equal to

• A. $3a+7b$
• B. 2b
• C. 0
• D. none of these.

Answer 1

Answer: (C)

Operating $R_2\to R_2-R_1$
and $R_3\to R_3-R_2,$ we get
$\left|\begin{array}{ccc}a& a+2b& a+4b\\ 2b& 2b& 2b\\ 2b& 2b& 2b\end{array}\right|$
which is certainly 0 as $R_2=R_3$.