If A=left[begin{array}{rrr}-1 & 2 & 3 5 & 7 | vedclass

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(A) First,calculate $A-B$:$A-B = \left[\begin{array}{rrr}-1 & 2 & 3 \ 5 & 7 & 9 \ -2 & 1 & 1\end{array}ight] - \left[\begin{array}{rrr}-4 & 1 & -5

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(A) First,calculate $A-B$:$A-B = \left[\begin{array}{rrr}-1 & 2 & 3 \ 5 & 7 & 9 \ -2 & 1 & 1\end{array}ight] - \left[\begin{array}{rrr}-4 & 1 & -5 \ 1 & 2 & 0 \ 1 & 3 & 1\end{array}ight] = \left[\begin{array}{rrr}3 & 1 & 8 \ 4 & 5 & 9 \ -3 & -2 & 0\end{array}ight]$Now,find the transpose $(A-B)^{\prime}$:$(A-B)^{\prime} = \left[\begin{array}{rrr}3 & 4 & -3 \ 1 & 5 & -2 \ 8 & 9 & 0\end{array}ight]$Next,find $A^{\prime}$ and $B^{\prime}$:$A^{\prime} = \left[\begin{array}{rrr}-1 & 5 & -2 \ 2 & 7 & 1 \ 3 & 9 & 1\end{array}ight]$,$B^{\prime} = \left[\begin{array}{rrr}-4 & 1 & 1 \ 1 & 2 & 3 \ -5 & 0 & 1\end{array}ight]$Now,calculate $A^{\prime}-B^{\prime}$:$A^{\prime}-B^{\prime} = \left[\begin{array}{rrr}-1 & 5 & -2 \ 2 & 7 & 1 \ 3 & 9 & 1\end{array}ight] - \left[\begin{array}{rrr}-4 & 1 & 1 \ 1 & 2 & 3 \ -5 & 0 & 1\end{array}ight] = \left[\begin{array}{rrr}3 & 4 & -3 \ 1 & 5 & -2 \ 8 & 9 & 0\end{array}ight]$Since $(A-B)^{\prime} = A^{\prime}-B^{\prime}$,the property is verified.

If $A=\left[\begin{array}{rrr}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{rrr}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right],$ then verify that $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.

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