Matrix Multiplication

         

Compute the following matrix multiplication: (2213)×(2413). \begin{pmatrix} 2 & 2 \\ 1 & 3 \end{pmatrix} \times \begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix}.

At an amusement park, tickets for the Pirate ship ride are $5.005.00 per adult and $9.009.00 per child. One sunny day, 558558 adults and 880880 children purchase tickets for this ride. The following day is rainy and only 219219 adults and 406406 children purchase tickets for this ride. By representing the number of rides in a matrix, calculate the total ticket sales (in dollars) for the ride over the two days.

Compute the following matrix multiplication: (223221)×(201231). \begin{pmatrix} 2 & 2 & 3 \\ 2 & 2 & 1 \end{pmatrix} \times \begin{pmatrix} 2 & 0 \\ 1 & 2 \\ 3 & 1 \end{pmatrix}.

Find the value of x+y x+ y which satisfies the following equation: (7132)×(xy)=(251). \begin{pmatrix} 7 & 1 \\ 3 & 2 \end{pmatrix} \times \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 \\ -51 \end{pmatrix}.

Find the 3×3 3 \times 3 matrix A A satisfying A×(110)=(556),A×(011)=(533),A×(101)=(643). A \times \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \\ 6 \end{pmatrix}, A \times \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 5 \\ 3 \\ 3 \end{pmatrix}, A \times \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \\ 3 \end{pmatrix}.

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