
Evaluate the following \[\left| {\begin{array}{*{20}{c}}
{15}&{11}&7 \\
{11}&{17}&{14} \\
{10}&{16}&{13}
\end{array}} \right|\]
Answer
591.9k+ views
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.
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.
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