2023-03-06

Can you multiply a $3x2$ and $2x2$ matrix?

gelo1368m6

Multiplication of matrix :
Let a matrix of order $m×n$ and another matrix $n×q$ when the number of columns in the first matrix equals the number of rows in the second matrix, the matrix can be multiplied.
Here we have to multiply $3×2$ matrix and $2×2$ matrix, which is possible and the resultant matrix will be $3×2$.
Let us understand with the help of an example.
Let $A=\left[\begin{array}{cc}0& 7\\ 3& 6\\ -2& 0\end{array}\right]$ and $B=\left[\begin{array}{cc}3& -4\\ 0& 12\end{array}\right]$
then, $\mathrm{AB}=\left[\begin{array}{cc}0×3+0×7& -4×0+7×12\\ 3×3+6×0& -4×3+6×12\\ -2×3+\left(-2\right)×0& -2×\left(-4\right)+12×0\end{array}\right]$$=\left[\begin{array}{cc}0& 84\\ 9& 60\\ -6& 8\end{array}\right]$
Therefore, In this way we can multiply the matrix.

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