Shirley Conrad

2023-03-06

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

gelo1368m6

Beginner2023-03-07Added 5 answers

Multiplication of matrix :

Let a matrix of order $m\times n$ and another matrix $n\times q$ 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 $3\times 2$ matrix and $2\times 2$ matrix, which is possible and the resultant matrix will be $3\times 2$.

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\times 3+0\times 7& -4\times 0+7\times 12\\ 3\times 3+6\times 0& -4\times 3+6\times 12\\ -2\times 3+(-2)\times 0& -2\times (-4)+12\times 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.

Let a matrix of order $m\times n$ and another matrix $n\times q$ 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 $3\times 2$ matrix and $2\times 2$ matrix, which is possible and the resultant matrix will be $3\times 2$.

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\times 3+0\times 7& -4\times 0+7\times 12\\ 3\times 3+6\times 0& -4\times 3+6\times 12\\ -2\times 3+(-2)\times 0& -2\times (-4)+12\times 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.