:−\BEGIN{gathered} \sf{2A + 2B = \left[\begin{array}{cc}2& - 1& 4 \\3 & 2 & 5\end{array}\right] } \\ \\ \sf{A + 2B = \left[\begin{array}{cc}5 & 0 & 3 \\1 & 6 & 2 \end{array}\right]}\end{gathered} 2A+2B=[ 23 −12 45 ] A+2B=[ 51 06 32 ] -----------------------\large \bf \clubs \: To \: Find :-♣ ToFind:−Value of 2B .-----------------------\large \bf \clubs \: Solution:-♣ Solution:−We Have,\begin{gathered} \pmb{2A + 2B = \left[\begin{array}{cc}2& - 1& 4 \\3 & 2 & 5\end{array}\right] } \: \: - - - - (1)\\ \\ \: \: \: \: \:\pmb{A + 2B = \left[\begin{array}{cc}5 & 0 & 3 \\1 & 6 & 2 \end{array}\right]} \: \: - - - - (2)\end{gathered} 2A+2B=[ 23 −12 45 ]2A+2B=[ 23 −12 45 ] − − − −(1) A+2B=[ 51 06 32 ]A+2B=[ 51 06 32 ] − − − −(2) Multiplying Eq. (2) by 2 We Get :\begin{gathered} \pmb{2A + 4B = \left[\begin{array}{cc}10 & 0 & 6 \\2 & 12 & 4\end{array}\right]} \: \: - - - - (3)\end{gathered} 2A+4B=[ 102 012 64 ]2A+4B=[ 102 012 64 ] − − − −(3) Subtracting (1) From (3) We Get :\begin{gathered} \sf \cancel{2A} + 4B - \cancel{2A} -2B \\ = \left[\begin{array}{cc}10 & 0 & 6 \\ 2 & 12 & 4\end{array}\right] - \left[\begin{array}{cc}2 & - 1 & 4 \\3 & 2 & 5\end{array}\right] \\ \\ :\longmapsto\sf2B = \left[\begin{array}{cc} 10- 2& 0+ 1& 6- 4 \\ 2- 3 & 12- 2 & 4 - 5\end{array}\right] \\ \\ \end{gathered} 2A +4B− 2A −2B =[ 102 012 64 ]−[ 23 −12 45 ] :⟼2B=[ 10−22−3 0+1 12−2 6− 44−5 ] \begin{gathered}\purple{ \large :\longmapsto \pmb{ \underline {\BOXED{{2B = \left[\begin{array}{cc} 8& 1& 2 \\ - 1 & 10 & - 1\end{array}\right]} }}}}\end{gathered} :⟼ 2B=[ 8−1 110 2 −1 ] 2B=[ 8−1 110 2 −1 ] \underline{\underline{\Large\pink{\mathfrak{ \text{H}ence \:\:option\:\: B\:\: Correct} }}} HenceoptionBCorrect \begin{gathered} \Large\red{\mathfrak{ \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}\end{gathered} Whichistherequired Answer. -----------------------