If \(x = \begin{pmatrix}1 & 2 \\ 0 & 3\end{pmatrix}\) and \(y = \begin{pmatrix}2 & 1 \\ 4 & 3\end{pmatrix}\). Find \(xy\).

Answer Details

To find xy, we need to perform matrix multiplication of x and y. To do this, we take the dot product of each row of x with each column of y, as follows: First row of x: (1 2 0 3) First column of y: ( 2 1 4 3 ) Dot product of the first row of x with the first column of y: 1*2 + 2*1 + 0*4 + 3*3 = 2 + 2 + 9 = 13 This gives us the first element of the product matrix. We repeat this process for the remaining rows and columns to get: xy = ( 1*2 + 2*1 + 0*4 + 3*3 1*1 + 2*4 + 0*3 + 3*2 1*4 + 2*3 + 0*2 + 3*1 1*3 + 2*2 + 0*1 + 3*4 0*2 + 3*1 + 1*4 + 2*3 0*1 + 3*4 + 1*3 + 2*2 0*4 + 3*3 + 1*2 + 2*1 0*3 + 3*2 + 1*1 + 2*4 ) = ( 13 11 10 17 11 19 13 14 ) Hence, xy = (107129). Therefore, the correct option is (A).