જો d in R, અને A = left[ {begin{array}{ | vedclass

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Question

$\left| A ight| = \left| {\begin{array}{*{20}{c}}
{ - 2}&{4 + d}&{\left( {\sin 	heta  - 2} ight)}\
1&{\left( {\sin 	heta } \

Vedclass · Accepted Answer

$-5$

Vedclass · Answer

$\left| A ight| = \left| {\begin{array}{*{20}{c}}
{ - 2}&{4 + d}&{\left( {\sin 	heta  - 2} ight)}\
1&{\left( {\sin 	heta } ight) + 2}&d\
5&{\left( {2\sin 	heta } ight) - d}&{\left( { - \sin 	heta } ight) + 2 + 2d}
\end{array}} ight|$

$ = \left| {\begin{array}{*{20}{c}}
{ - 2}&{4 + d}&{\left( {\sin 	heta  - 2} ight)}\
1&{\left( {\sin 	heta } ight)}&d\
1&0&0
\end{array}} ight|$            (New ${R_3} = {R_3} - 2{R_2} + {R_1}$)

$ = \left( {4 + d} ight)d - {\sin ^2}	heta  + 4 = {\left( {d + 2} ight)^2} - {\sin ^2}	heta $

Because minimum value of $\left| A ight| = 8 \Rightarrow {\left( {d + 2} ight)^2} = 9 \Rightarrow d = 1$ or $-5$

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