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 $AB$ possible ? Given a reason. If yes, find $AB.$
✓
Answer
$A =\left[\begin{array}{cc}3 & 5 \\ 4 & -2\end{array}\right]_{2 \times 2}$ and $B =\left[\begin{array}{l}2 \\ 4\end{array}\right]_{2 \times 1}$
the product $AB$ is possible as the number of columns in $A$ are equal to the number of rows in $B.$
Now $AB =\left[\begin{array}{cc}3 & 5 \\ 4 & -2\end{array}\right]\left[\begin{array}{l}2 \\ 4\end{array}\right]$
$\begin{array}{l}=\left[\begin{array}{c}3 \times 2+5 \times 4 \\ 4 \times 2+(-2) \times 4\end{array}\right] \\\end{array} $
$=\left[\begin{array}{c}26 \\ 0\end{array}\right] .$
the product $AB$ is possible as the number of columns in $A$ are equal to the number of rows in $B.$
Now $AB =\left[\begin{array}{cc}3 & 5 \\ 4 & -2\end{array}\right]\left[\begin{array}{l}2 \\ 4\end{array}\right]$
$\begin{array}{l}=\left[\begin{array}{c}3 \times 2+5 \times 4 \\ 4 \times 2+(-2) \times 4\end{array}\right] \\\end{array} $
$=\left[\begin{array}{c}26 \\ 0\end{array}\right] .$
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