Question 371 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.

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

Marking scheme

  1. 1.1 mark: correct 3×33 \times 3 sales matrix with all nine quantities placed correctly (rows = items, columns = schools, or the labelled transpose).
  2. 2.Accept 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.

Common mistakes

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

Analysis and 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.

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.

Question details

Q37 of 44 questions

Board
CBSE
Class
Class 12
Subject
Applied Mathematics
Year
2026
Section
Section E
Marks
1
Chapter
Matrices
Topic
Matrix Representation of Quantities Sold
Bloom's level
understand
Syllabus topic
Unit 2: Algebra — Matrices: Formation and Representation of Data as a Matrix
Author
CBSE
Reviewed by
Padhantu Academic Team

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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.