Question

Let the given determinant be ( Delta ). Then ( Delta=left|begin{array}{ccc}265 & 240 & 219 240 & 225 & 198 219 & 198 & 181end{array}right| )
( =left|begin{array}{ccc}46 & 21 & 219 42 & 27 & 198 38 & 17 & 181end{array}right| quadleft[C_{1} rightarrowleft(C_{1}-C_{3}right) text { and } C_{2} rightarrowleft(C_{2}-C_{3}right)right] )
( =left|begin{array}{rrr}4 & 21 & 9 -12 & 27 & -72 4 & 17 & 11end{array}right| quadleft[C_{1} rightarrowleft(C_{1}-2 C_{2}right) text { and } C_{3} rightarrowleft(C_{3}-10 C_{2}right)right] )
( left.=left|begin{array}{rrr}0 & 4 & -2 0 & 78 & -39 4 & 17 & 11end{array}right| quad quad quad quad quad R_{1} rightarrowleft(R_{1}-R_{3}right) text { and } R_{2} rightarrowleft(R_{2}+3 R_{3}right)right} )
( =2(39)left|begin{array}{rrr}0 & 2 & -1 0 & 2 & -1 4 & 17 & 11end{array}right| )
[taking ( left.2 text { common from } R_{1} text { and } 39 text { common from } R_{2}rightrceil ) ( =(78 times 0)=0 )
( left[because R_{1} text { and } R_{2} ) are identical] right.

# EXAMPLE 1 Evaluate 265 240 219 240 225 198 219 198 181

Solution