Question

Write and label a matrix to organize the information. Music Store Inventory: cos: 52 sale price titles, 3300 regular price titles Tapes: 28 sale price titles, 1600 regular price titles

Short answer

The completed and labeled matrix representing the music store inventory is: \[\begin{array}{c|cc} & \text{Sale Price Titles} & \text{Regular Price Titles} \ \hline \text{CDs} & 52 & 3300 \ \text{Tapes} & 28 & 1600 \end{array}\].

Step-by-step solution

Define the Rows and Columns of the Matrix

In this problem, the rows of the matrix will be defined by the type of music: CDs and Tapes. The columns will be defined by the price status of the music: sale price titles and regular price titles.

Enter the Data

The data given in the problem corresponds to the number of titles for each type of music and price status. For CDs there are 52 sale price titles and 3300 regular price titles. For Tapes, there are 28 sale price titles and 1600 regular price titles.

Create the Matrix

In writing the matrix, the first row will represent CDs and the second row will represent Tapes. The first column will represent sale price titles and the second column will represent regular price titles. Thus, the matrix becomes: \[\left[\begin{array}{cc}52 & 3300 \28 & 1600\end{array}\right]\]. This matrix is read as follows: CDs have 52 sale price titles and 3300 regular price titles. Tapes have 28 sale price titles and 1600 regular price titles.

Label the Matrix

The final step is to label the matrix according to the type of music and price status. The completed and labeled matrix becomes: \[\begin{array}{c|cc} & \text{Sale Price Titles} & \text{Regular Price Titles} \ \hline \text{CDs} & 52 & 3300 \ \text{Tapes} & 28 & 1600 \end{array}\].