यदि A^ = [ cc -2 & 3 1 & 2 ] तथा B = [ rr -1 & 0 1 & 2 ] हैं तो (A + 2B)^ ज्ञात कीजिए।

दिया है, A^ = [ rr -2 & 3 1 & 2 ] A = (A^ )^ = [ rr -2 & 3 1 & 2 ]^ = [ rr -2 & 1 3 & 2 ][ (A^ )^ = A] तथा 2B = 2 [ rr -1 & 0 1 & 2 ] = [ rr -2 & 0 2 & 4 ] A + 2B = [ rr -2 & 1 3 & 2 ] + [ rr -2 & 0 2 & 4 ] = [ rr -4 & 1 5 & 6 ] (A + 2B)^ = [ rr -4 & 1 5 & 6 ] = [ rr -4 & 5 1 & 6 ]

यदि A^ = [ cc -2 & 3 1 & 2 ] तथा B = [ rr -1 & 0 1 & 2 ] हैं तो (…

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यदि $ \mathrm{A}^{\prime}$ = $\left[\begin{array}{cc} -2 & 3 \\ 1 & 2 \end{array}\right] $ तथा B = $ \left[\begin{array}{rr} -1 & 0 \\ 1 & 2 \end{array}\right] $ हैं तो (A + 2B)$^{\prime}$ ज्ञात कीजिए।

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दिया है, A$^{\prime}$ = $ \left[\begin{array}{rr} -2 & 3 \\ 1 & 2 \end{array}\right]$
$\Rightarrow$ A = $ \left(A^{\prime}\right)^{\prime}$ = $ \left[\begin{array}{rr}-2 & 3 \\ 1 & 2\end{array}\right]^{\prime}$ = $\left[\begin{array}{rr}-2 & 1 \\ 3 & 2\end{array}\right]$[$\because$ $(A^{\prime})^{\prime}$ = A]
तथा 2B = $2\left[\begin{array}{rr} -1 & 0 \\ 1 & 2 \end{array}\right]$ = $ \left[\begin{array}{rr} -2 & 0 \\ 2 & 4 \end{array}\right]$
$\therefore$ A + 2B = $ \left[\begin{array}{rr} -2 & 1 \\ 3 & 2 \end{array}\right]$ + $\left[\begin{array}{rr} -2 & 0 \\ 2 & 4 \end{array}\right]$ = $\left[\begin{array}{rr} -4 & 1 \\ 5 & 6 \end{array}\right] $
$\Rightarrow$ (A + 2B)$^{\prime}$ = $\left[\begin{array}{rr} -4 & 1 \\ 5 & 6 \end{array}\right]$ = $\left[\begin{array}{rr} -4 & 5 \\ 1 & 6 \end{array}\right] $

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