Q37
1 markSection E

What is the sales matrix ?

Matrices
Matrix Representation of Quantities Sold
Official Answer

The sales matrix records how many of each article each school sold, taken straight from the table.


Sales (quantity) matrix Q — rows = items (fans, mats, plates), columns = schools (A, B, C):


Item \ SchoolABC
Fans503035
Mats603540
Plates405025

Q=[503035603540405025]Q = \begin{bmatrix}50 & 30 & 35 \\ 60 & 35 & 40 \\ 40 & 50 & 25\end{bmatrix}, a 3×33 \times 3 matrix.

sales matrixquantity matrix3x3 matrixarticles soldschools A B Cmatrix from tablefans mats plates

Marking Scheme

  • 11 mark: correct 3×33 \times 3 sales matrix with all nine quantities placed correctly (rows = items, columns = schools, or the labelled transpose).
  • 2Accept the transpose provided rows/columns are clearly labelled.

Hint

Arrange the quantities in a 3×33 \times 3 matrix with rows for the items (fans, mats, plates) and columns for the schools (A, B, C), reading directly from the table.

Quick Oral Answer

The sales matrix is the 3 by 3 grid of quantities — rows for fans, mats and plates, columns for schools A, B and C — read directly from the table.

Analysis & Explanation

This part checks tabulation-to-matrix conversion, the second building block of the case study.


Concept


  • The 3×33 \times 3 sales matrix simply reproduces the data table; rows index the three articles and columns index the three schools (or vice versa — either convention is acceptable if stated).
  • Choosing rows = items keeps it conformable for premultiplication by the 1×31 \times 3 price row matrix, giving a 1×31 \times 3 funds-by-school matrix.

Exam trap


  • Mixing up rows and columns (transposing accidentally) changes which number belongs to which school; always label the matrix.

Real-world


  • Sales matrices like this are the standard way point-of-sale systems store multi-outlet, multi-product data before aggregating revenue.

Common Mistakes

  1. 1Transposing the matrix without labelling, so school and item entries get swapped.
  2. 2Copying a column of the data table incorrectly (a single misplaced number costs the mark).
  3. 3Confusing the sales matrix with the price matrix from part (i).

Interesting Facts

Storing sales as a matrix lets total revenue across all schools be found with one matrix product, showing why linear algebra underpins business analytics.

A matrix whose rows and columns both carry meaning (items vs outlets) is called a data or contingency matrix, widely used in statistics.

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Frequently Asked Questions

Can I write the sales matrix with schools as rows instead of items?

Yes, the transpose is equally valid as long as you clearly label which axis is schools and which is items. Just make sure the orientation stays conformable with the price matrix when you multiply them to find funds.

What is the order of the sales matrix?

It is a 3×33 \times 3 matrix — three items (fans, mats, plates) and three schools (A, B, C) — containing nine quantity entries.