X तथा Y, ज्ञात कीजिए, यदि X + Y = $ \left[\begin{array}{ll} 5 & 2 \\ 0 & 9 \end{array}\right] $ तथा X - Y =$ \left[\begin{array}{cc} 3 & 6 \\ 0 & -1 \end{array}\right] $ है।
EXAMPLE-9
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यहाँ पर (X + Y) + (X - Y) = $ \left[\begin{array}{ll} 5 & 2 \\ 0 & 9 \end{array}\right]$ + $\left[\begin{array}{cc} 3 & 6 \\ 0 & -1 \end{array}\right]$
या (X + X) + (Y - Y) =$ \left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right] $ $\Rightarrow$ 2X = $ \left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right]$
या X = $ \frac{1}{2}$$\left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right]$ = $\left[\begin{array}{ll} 4 & 4 \\ 0 & 4 \end{array}\right] $
साथ ही (X + Y) - (X - Y) = $\left[\begin{array}{ll} 5 & 2 \\ 0 & 9 \end{array}\right]$ - $ \left[\begin{array}{rr} 3 & 6 \\ 0 & -1 \end{array}\right] $
या (X - X) + (Y + Y) = $\left[\begin{array}{cc} 5-3 & 2-6 \\ 0 & 9+1 \end{array}\right] $$ \Rightarrow$ 2Y = $\left[\begin{array}{cc} 2 & -4 \\ 0 & 10 \end{array}\right] $
या Y = $\frac{1}{2}$$\left[\begin{array}{rr} 2 & -4 \\ 0 & 10 \end{array}\right]$ = $\left[\begin{array}{rr} 1 & -2 \\ 0 & 5 \end{array}\right]$
या (X + X) + (Y - Y) =$ \left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right] $ $\Rightarrow$ 2X = $ \left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right]$
या X = $ \frac{1}{2}$$\left[\begin{array}{ll} 8 & 8 \\ 0 & 8 \end{array}\right]$ = $\left[\begin{array}{ll} 4 & 4 \\ 0 & 4 \end{array}\right] $
साथ ही (X + Y) - (X - Y) = $\left[\begin{array}{ll} 5 & 2 \\ 0 & 9 \end{array}\right]$ - $ \left[\begin{array}{rr} 3 & 6 \\ 0 & -1 \end{array}\right] $
या (X - X) + (Y + Y) = $\left[\begin{array}{cc} 5-3 & 2-6 \\ 0 & 9+1 \end{array}\right] $$ \Rightarrow$ 2Y = $\left[\begin{array}{cc} 2 & -4 \\ 0 & 10 \end{array}\right] $
या Y = $\frac{1}{2}$$\left[\begin{array}{rr} 2 & -4 \\ 0 & 10 \end{array}\right]$ = $\left[\begin{array}{rr} 1 & -2 \\ 0 & 5 \end{array}\right]$
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