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

  • A \(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)
  • B \(\begin{pmatrix} 2 & 7 \\ 4 & 17 \end{pmatrix}\)
  • C \(\begin{pmatrix} 10 & 4 \\ 4 & 6 \end{pmatrix}\)
  • D \(\begin{pmatrix} 4 & 3 \\ 10 & 9 \end{pmatrix}\)

The correct answer is A. \(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)

The product of two matrices is obtained by taking the dot product of each row of the first matrix with each column of the second matrix. In this case, we have:

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

So, the product xy is given by:

xy = (\begin{pmatrix} 1 & 2 \ 0 & 3 \end{pmatrix}) * (\begin{pmatrix} 2 & 1 \ 4 & 3 \end{pmatrix}) = (\begin{pmatrix} (1)(2) + (2)(4) & (1)(1) + (2)(3) \ (0)(2) + (3)(4) & (0)(1) + (3)(3) \end{pmatrix}) = (\begin{pmatrix} 10 & 7 \ 12 & 9 \end{pmatrix})

So, the product of the two matrices x and y is (\begin{pmatrix} 10 & 7 \ 12 & 9 \end{pmatrix}). 

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