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જો $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1\end{array}\right]$ અને $B=\left[\begin{array}{rrr}3 & -1 & 3 \\ -1 & 0 & 2\end{array}\right] $ તો $2A -B$ શોધો.
$\left[\begin{array}{ccc}1 & 5 & 3 \\ 5 & 6 & 0\end{array}\right]$
$\left[\begin{array}{ccc}-1 & 5 & 3 \\ 5 & -6 & 0\end{array}\right]$
$\left[\begin{array}{ccc}-1 & 5 & 3 \\ 5 & 6 & 0\end{array}\right]$
$\left[\begin{array}{ccc}-1 & 5 & -3 \\ 5 & -6 & 0\end{array}\right]$
Solution
We have
$2 A-B=2\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1\end{array}\right]-\left[\begin{array}{ccc}3 & -1 & 3 \\ -1 & 0 & 2\end{array}\right]$
$=\left[\begin{array}{lll}2 & 4 & 6 \\ 4 & 6 & 2\end{array}\right]+\left[\begin{array}{ccc}-3 & 1 & -3 \\ 1 & 0 & -2\end{array}\right]$
$=\left[\begin{array}{lll}2-3 & 4+1 & 6-3 \\ 4+1 & 6+0 & 2-2\end{array}\right]=\left[\begin{array}{ccc}-1 & 5 & 3 \\ 5 & 6 & 0\end{array}\right]$
