# For each of the pairs of matrices that follow, determine whether it is possible to multiply the first matrix times the second. If it is possible, perform the multiplication. begin{bmatrix}1 & 4&3 0 & 1&40&0&2 end{bmatrix}begin{bmatrix}3 & 2 1 & 14&5 end{bmatrix}

Matrices
For each of the pairs of matrices that follow, determine whether it is possible to multiply the first matrix times the second. If it is possible, perform the multiplication.
$$\begin{bmatrix}1 & 4&3 \\0 & 1&4\\0&0&2 \end{bmatrix}\begin{bmatrix}3 & 2 \\1 & 1\\4&5 \end{bmatrix}$$

2020-10-28
Given,
$$\begin{bmatrix}1 & 4&3 \\0 & 1&4\\0&0&2 \end{bmatrix}\begin{bmatrix}3 & 2 \\1 & 1\\4&5 \end{bmatrix}$$
Here the order of first matrix is ($$3 \times 3$$) and the order of second matrix is ($$3 \times 2$$), therefore the number of columns of first matrix(3) is equal to number of rows of second matrix(3).
Hence multiplication of these matrices is possible.
Therefore,
$$\begin{bmatrix}1 & 4&3 \\0 & 1&4\\0&0&2 \end{bmatrix}\begin{bmatrix}3 & 2 \\1 & 1\\4&5 \end{bmatrix}=\begin{bmatrix}1(3)+4(1)+3(4) & 1(2)+4(1)+3(5) \\0(3)+1(1)+4(4) & 0(2)+1(1)+4(5)\\0(3)+0(1)+2(4)&0(2)+0(1)+2(5) \end{bmatrix}$$
$$=\begin{bmatrix}19 & 21 \\17 & 21\\8&10 \end{bmatrix}$$