Question

Find the value of

$A=\left|\begin{array}{ccc}1& 5& 7\\ 5& 25& 35\\ 12& 20& 24\end{array}\right|$

• A. $100$
• B. $33$
• C. $22$
• D. $99$

Answer 1

The correct option is A $100$

$A=\left[\begin{array}{ccc}1& 5& 2\\ 5& 25& 35\\ 12& 20& 24\end{array}\right]$

$=1(25\times 24-20\times 35)-5(5\times 24-35\times 12)+7(5\times 20-25\times 12)=(600-700)-5(100-420)+7(100-300)=-100+1600+7(-200)=-100+1600-1400=100$