Question
If $A=\left[\begin{array}{cc}3 & 5 \\ 4 & -2\end{array}\right]$ and $B=\left[\begin{array}{l}2 \\ 4\end{array}\right]$, is the product $A B$ possible? Give a reason. If yes, find $A B.$
✓
Answer
Yes, the product is possible because of
number of column in $A=$ number of row in $B$
i.e. $(2 \times 2) .(2 \times 1)=(2 \times 1)$ is the order of the matrix.
$ \begin{aligned} & AB =\left[\begin{array}{cc} 3 & 5 \\ 4 & -2 \end{array}\right]\left[\begin{array}{l} 2 \\ 4 \end{array}\right] \end{aligned} $
$ =\left[\begin{array}{c} 3 \times 2+5 \times 4 \\ 4 \times 2+(-2) \times 4 \end{array}\right] $
$ =\left[\begin{array}{c} 6+20 \\ 8-8 \end{array}\right] $
$ =\left[\begin{array}{c} 26 \\ 0 \end{array}\right] .$
number of column in $A=$ number of row in $B$
i.e. $(2 \times 2) .(2 \times 1)=(2 \times 1)$ is the order of the matrix.
$ \begin{aligned} & AB =\left[\begin{array}{cc} 3 & 5 \\ 4 & -2 \end{array}\right]\left[\begin{array}{l} 2 \\ 4 \end{array}\right] \end{aligned} $
$ =\left[\begin{array}{c} 3 \times 2+5 \times 4 \\ 4 \times 2+(-2) \times 4 \end{array}\right] $
$ =\left[\begin{array}{c} 6+20 \\ 8-8 \end{array}\right] $
$ =\left[\begin{array}{c} 26 \\ 0 \end{array}\right] .$
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