Question

please help me to solve this ​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

Find the value of

$\rm :\longmapsto\:\begin{array}{|cc|}\sf - 1 &\sf 7 \\ \sf 2 &\sf 4 \\\end{array}$

$\red{\large\underline{\sf{Solution-}}}$

Given determinant is

$\rm :\longmapsto\:\begin{array}{|cc|}\sf - 1 &\sf 7 \\ \sf 2 &\sf 4 \\\end{array}$

$\rm \:  =  \: ( - 1) \times 4 - 2 \times 7$

$\rm \:  =  \: - 4 - 14$

$\rm \:  =  \: - \: 18$

Hence,

The value of

$\rm :\longmapsto\:\boxed{ \bf{ \: \: \:\begin{array}{|cc|}\sf - 1 &\sf 7 \\ \sf 2 &\sf 4 \\\end{array} \: = \: - \: 18 \: \: \: }}$

Additional Information :-

$\red{\rm :\longmapsto\: |AB| = |A| \: |B| }$

$\red{\rm :\longmapsto\: |kA| = {k}^{n} |A|}$

$\red{\rm :\longmapsto\: |kAB| = {k}^{n} |A| \: |B| }$

$\red{\rm :\longmapsto\: |adjA| \: = \: { |A| }^{n - 1}}$

$\red{\rm :\longmapsto\: |A \: adjA| \: = \: { |A| }^{n}}$

$\red{\rm :\longmapsto\: | {A}^{ - 1} | \: = \: \dfrac{1}{ |A| }}$

$\red{\rm :\longmapsto\: |A'| = |A|}$