# 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}

Question
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,
$$\begin{bmatrix}1 & 4&3 \\0 & 1&4\\0&0&2 \end{bmatrix}\begin{bmatrix}3 & 2 \\1 & 1\\4&5 \end{bmatrix}=\begin{bmatrix}1(3)+4(1)+3(4) & 1(2)+4(1)+3(5) \\0(3)+1(1)+4(4) & 0(2)+1(1)+4(5)\\0(3)+0(1)+2(4)&0(2)+0(1)+2(5) \end{bmatrix}$$
$$=\begin{bmatrix}19 & 21 \\17 & 21\\8&10 \end{bmatrix}$$

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