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

{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.