Question

$\left|\begin{array}{ccc}a+b& a+2b& a+3b\\ a+2b& a+3b& a+4b\\ a+4b& a+5b& a+6b\end{array}\right|=$

• A. $a^2+b^2+c^2-3abc$
• B. 3ab
• C. 3a+5b

Answer 1

$\left|\begin{array}{ccc}a+b& a+2b& a+3b\\ a+2b& a+3b& a+4b\\ a+4b& a+5b& a+6b\end{array}\right|=\left|\begin{array}{ccc}a+b& a+2b& a+3b\\ b& b& b\\ 2b& 2b& 2b\end{array}\right|=0by\left\{\begin{array}{c}{R}_2\to R_2-R_1\\ R_3\to R_3-R_2\end{array}\right\}$
Trick : Putting a=1=b. The determinant will be $\left|\begin{array}{ccc}2& 3& 4\\ 3& 4& 5\\ 5& 6& 7\end{array}\right|=0$.