Which of the following product of matrices are conformable for multiplication?

Question

Question:

Which of the following product of matrices are conformable for multiplication?

(i) $\left[ \begin{matrix} 1 & -1 \ 0 & 2 \ \end{matrix} ight]\left[ \begin{matrix} -2 \ 3 \ \end{matrix} ight]$

(ii) $\left[ \begin{matrix} 1 & -1 \ 1 & 0 \ \end{matrix} ight]\left[ \begin{matrix} 2 & -1 \ 1 & 3 \ \end{matrix} ight]$

(iii) $\left[ \begin{matrix} 1 \ -1 \ \end{matrix} ight]\left[ \begin{matrix} 0 & 1 \ -1 & 2 \ \end{matrix} ight]$

(iv) $\left[ \begin{matrix} 1 & 2 \ 0 & -1 \ -1 & -2 \ \end{matrix} ight]\left[ \begin{matrix} 1 & 0 & -1 \ 0 & 1 & 2 \ \end{matrix} ight]$

(v) $\left[ \begin{matrix} 3 & 2 & 1 \ 0 & 1 & -1 \ \end{matrix} ight]\left[ \begin{matrix} 1 & -1 \ 0 & 2 \ -2 & 3 \ \end{matrix} ight]$

Accepted Answer

Solution:
Two matrices are conformable for multiplication if the numbers of columns of first matrix are equal to number of rows of second matrix. So, according to this definition:

(i) is conformable for multiplication (because the first matrix has two columns and second matrix has same number of rows).

(ii) is conformable for multiplication (because the first matrix has two columns and second matrix has same number of rows).

(iii) is not conformable for multiplication (because the first matrix has just one column and second matrix has two rows).

(iv) is conformable for multiplication (because the first matrix has just two columns and second matrix has the same number of rows).

(v) is conformable for multiplication (because the first matrix has three columns and second matrix has same number of rows).