Question

Evaluate the following \[\left| {\begin{array}{*{20}{c}}
  {15}&{11}&7 \\
  {11}&{17}&{14} \\
  {10}&{16}&{13}
\end{array}} \right|\]

Answer 1

Hint: Here we will find the value of determinant by expanding the determinant over Row 1.

Complete step-by-step answer:

You have to find out the value of
\[\left| {\begin{array}{*{20}{c}}
  {15}&{11}&7 \\
  {11}&{17}&{14} \\
  {10}&{16}&{13}
\end{array}} \right|\]
Expanding this determinant over Row 1
$
   \Rightarrow 15\left| {\begin{array}{*{20}{c}}
  {17}&{14} \\
  {16}&{13}
\end{array}} \right| - 11\left| {\begin{array}{*{20}{c}}
  {11}&{14} \\
  {10}&{13}
\end{array}} \right| + 7\left| {\begin{array}{*{20}{c}}
  {11}&{17} \\
  {10}&{16}
\end{array}} \right| \\
   \Rightarrow 15(17 \times 13 - 16 \times 14) - 11(11 \times 13 - 10 \times 14) + 7(11 \times 16 - 10 \times 17) \\
   \Rightarrow 15( - 3) - 11(3) + 7(6) \\
   \Rightarrow - 45 - 33 + 42 \\
   \Rightarrow - 36 \\
$
So, this is your required value of the determinant.

Note: Whenever this type of questions are given first find out its co - factors for any column or row terms and then simplify it using the above rule we will get the solution for the determinant.