यदि A = [ rrr 1 & 2 & -3 5 & 0 & 2 1 & -1 & 1 ], B = [ rrr 3 & -1 & 2 4 & 2 & 5 2 & 0 & 3 ] तथा C = [ rrr 4 & 1 & 2 0 & 3 & 2 1 & -2 & 3 ], तो (A + B) तथा (B - C) परिकलित कीजिए। साथ ही सत्यापित कीजिए कि A + (B - C) = (A + B) - C.

A + B = [ rrr 1 & 2 & -3 5 & 0 & 2 1 & -1 & 1 ] + [ rrr 3 & -1 & 2 4 & 2 & 5 2 & 0 & 3 ] = [ rrr 4 & 1 & -1 9 & 2 & 7 3 & -1 & 4 ] तथा B - C = [ ccc 3 & -1 & 2 4 & 2 & 5 2 & 0 & 3 ] - [ ccc 4 & 1 & 2 0 & 3 & 2 1 & -2 & 3 ]= [ rrr -1 & -2 & 0 4 & -1 & 3 1 & 2 & 0 ] (A + B) - C = [ rrr 4 & 1 & -1 9 & 2 & 7 3 & -1 & 4 ] - [ rrr 4 & 1 & 2 0 & 3 & 2 1 & -2 & 3 ]= [ rrr 0 & 0 & -3 9 & -1 & 5 2 & 1 & 1 ] तथा A + (B - C) = [ rrr 1 & 2 & -3 5 & 0 & 2 1 & -1 & 1 ] + [ rrr -1 & -2 & 0 4 & -1 & 3 1 & 2 & 0 ] = [ rrr 0 & 0 & -3 9 & -1 & 5 2 & 1 & 1 ] अतः (A + B) - C = A + (B - C) सत्य है।

यदि A = [ rrr 1 & 2 & -3 5 & 0 & 2 1 & -1 & 1 ], B = [ rrr 3 & -1…

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यदि A = $\left[\begin{array}{rrr}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1\end{array}\right]$, B = $ \left[\begin{array}{rrr}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right]$ तथा C = $\left[\begin{array}{rrr}4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -2 & 3\end{array}\right]$, तो (A + B) तथा (B - C) परिकलित कीजिए। साथ ही सत्यापित कीजिए कि A + (B - C) = (A + B) - C.

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Answer

A + B = $\left[\begin{array}{rrr} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{array}\right]$ + $ \left[\begin{array}{rrr} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{array}\right]$ = $\left[\begin{array}{rrr} 4 & 1 & -1 \\ 9 & 2 & 7 \\ 3 & -1 & 4 \end{array}\right]$
तथा B - C = $ \left[\begin{array}{ccc} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{array}\right]$ - $\left[\begin{array}{ccc} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -2 & 3 \end{array}\right]$= $\left[\begin{array}{rrr} -1 & -2 & 0 \\ 4 & -1 & 3 \\ 1 & 2 & 0 \end{array}\right]$
$\therefore$ (A + B) - C =$ \left[\begin{array}{rrr} 4 & 1 & -1 \\ 9 & 2 & 7 \\ 3 & -1 & 4 \end{array}\right]$ - $\left[\begin{array}{rrr} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -2 & 3 \end{array}\right]$= $\left[\begin{array}{rrr} 0 & 0 & -3 \\ 9 & -1 & 5 \\ 2 & 1 & 1 \end{array}\right]$
तथा A + (B - C) = $ \left[\begin{array}{rrr}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1\end{array}\right]$ + $\left[\begin{array}{rrr}-1 & -2 & 0 \\ 4 & -1 & 3 \\ 1 & 2 & 0\end{array}\right]$ = $\left[\begin{array}{rrr}0 & 0 & -3 \\ 9 & -1 & 5 \\ 2 & 1 & 1\end{array}\right]$
अतः (A + B) - C = A + (B - C) सत्य है।

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