यदि A^ = [ rr 3 & 4 -1 & 2 0 & 1 ] तथा B = [ rrr -1 & 2 & 1 1 & 2 & 3 ] हैं तो सत्यापित कीजिए कि (A - B)^ = A^ - B^

A = (A^ )^ = [ rr 3 & 4 -1 & 2 0 & 1 ]^ = [ ccc 3 & -1 & 0 4 & 2 & 1 ] यहाँ, दायाँ पक्ष = A^ - B^ = [ rr 3 & 4 -1 & 2 0 & 1 ] - [ rr -1 & 1 2 & 2 1 & 3 ] = [ rr 3+1 & 4-1 -1-2 & 2-2 0-1 & 1-3 ] = [ rr 4 & 3 -3 & 0 -1 & -2 ] तथा (A - B)^ = ( [ ccc 3 & -1 & 0 4 & 2 & 1 ]- [ ccc -1 & 2 & 1 1 & 2 & 3 ] )^ [ A = (A^ )^ ] = [ ccc 3+1 & -1-2 & 0-1 4-1 & 2-2 & 1-3 ] = [ ccc 4 & -3 & -1 3 & 0 & -2 ]^ = [ cc 4 & 3 -3 & 0 -1 & -2 ] अतः (A - B)^ = A^ - B^ सत्यापित हुआ।

यदि A^ = [ rr 3 & 4 -1 & 2 0 & 1 ] तथा B = [ rrr -1 & 2 & 1 1 & 2…

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Question

यदि $\mathrm{A}^{\prime}$ = $ \left[\begin{array}{rr} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{array}\right]$ तथा B = $ \left[\begin{array}{rrr} -1 & 2 & 1 \\ 1 & 2 & 3 \end{array}\right] $ हैं तो सत्यापित कीजिए कि (A - B)$^{\prime}$ = A$^{\prime}$ - B$^{\prime}$

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Answer

$\because$ A = $\left(A^{\prime}\right)^{\prime}$ = $\left[\begin{array}{rr} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{array}\right]^{\prime}$ = $ \left[\begin{array}{ccc} 3 & -1 & 0 \\ 4 & 2 & 1 \end{array}\right]$
यहाँ, दायाँ पक्ष = A$^{\prime}$ - B$^{\prime}$ =$ \left[\begin{array}{rr}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ - $\left[\begin{array}{rr}-1 & 1 \\ 2 & 2 \\ 1 & 3\end{array}\right]$ = $\left[\begin{array}{rr}3+1 & 4-1 \\ -1-2 & 2-2 \\ 0-1 & 1-3\end{array}\right]$ = $ \left[\begin{array}{rr}4 & 3 \\ -3 & 0 \\ -1 & -2\end{array}\right]$
तथा (A - B)$^{\prime}$ = $\left(\left[\begin{array}{ccc}3 & -1 & 0 \\ 4 & 2 & 1\end{array}\right]-\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right]\right)^{\prime}$[$\because $ A =$ \left(A^{\prime}\right)^{\prime}$]
= $ \left[\begin{array}{ccc}3+1 & -1-2 & 0-1 \\ 4-1 & 2-2 & 1-3\end{array}\right]$ = $\left[\begin{array}{ccc}4 & -3 & -1 \\ 3 & 0 & -2\end{array}\right]^{\prime}$= $\left[\begin{array}{cc}4 & 3 \\ -3 & 0 \\ -1 & -2\end{array}\right]$
अतः (A - B)$^{\prime}$ = A$^{\prime}$ - B$^{\prime}$ सत्यापित हुआ।