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Matrices

Matrix Multiplication

Compute the following matrix multiplication: \[ \begin{pmatrix} 2 & 2 \\ 1 & 3 \end{pmatrix} \times \begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix}. \]

At an amusement park, tickets for the Pirate ship ride are $\(5.00\) per adult and $\(9.00\) per child. One sunny day, \(558\) adults and \(880\) children purchase tickets for this ride. The following day is rainy and only \(219\) adults and \(406\) 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: \[ \begin{pmatrix} 2 & 2 & 3 \\ 2 & 2 & 1 \end{pmatrix} \times \begin{pmatrix} 2 & 0 \\ 1 & 2 \\ 3 & 1 \end{pmatrix}. \]

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

Find the \( 3 \times 3 \) matrix \( A \) satisfying \[ A \times \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \\ 6 \end{pmatrix}, A \times \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 5 \\ 3 \\ 3 \end{pmatrix}, A \times \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \\ 3 \end{pmatrix}. \]

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