Question 361 markSection E

What is the price matrix ?

Matrices
Matrix Representation of Prices

Official answer

The price matrix lists the selling price of each item — fans Rs 25, mats Rs 50, plates Rs 10.


As a row matrix (1×31 \times 3):


P=[255010]P = \begin{bmatrix}25 & 50 & 10\end{bmatrix}


Or equivalently as a column matrix (3×13 \times 1):


P=[255010]P = \begin{bmatrix}25 \\ 50 \\ 10\end{bmatrix} (fans, mats, plates in order)


Price matrix P=[255010]P = \begin{bmatrix}25 & 50 & 10\end{bmatrix}.

Answer keywords:price matrixrow matrixcolumn matrixorder 1x3fans mats platesmatrix representationcost per article

Marking scheme

  1. 1.1 mark: correctly writing the price matrix [255010]\begin{bmatrix}25 & 50 & 10\end{bmatrix} (row) or its column equivalent, with items in a consistent order.
  2. 2.Accept either orientation as long as the three prices 25, 50, 10 appear correctly.

Hint

There are three items — fans, mats, plates — each with one price. Write these three prices as a single-row (1×31 \times 3) or single-column (3×13 \times 1) matrix in the order fans, mats, plates.

Quick oral answer

The price matrix is just the three selling prices arranged in order — [255010]\begin{bmatrix}25 & 50 & 10\end{bmatrix} for fans, mats and plates — as a 1 by 3 row matrix.

Common mistakes

  1. 1.Writing the prices in a different order than the sales matrix uses, which breaks conformability later.
  2. 2.Confusing the price matrix with the sales (quantity) matrix.
  3. 3.Giving a 3×33 \times 3 matrix instead of a single row/column of three prices.

Analysis and explanation

This opening part of the case study checks whether a student can translate given numerical data into matrix form.


Concept


  • A matrix is simply a rectangular arrangement of numbers; here the three prices form a 1×31 \times 3 row matrix (or a 3×13 \times 1 column matrix).
  • The chosen orientation matters for later parts: to multiply price × quantity and get funds, the price matrix must be conformable with the sales matrix, so a row price matrix [255010]\begin{bmatrix}25 & 50 & 10\end{bmatrix} pairs with a column of quantities.

Exam trap


  • Keep the item order consistent (fans, mats, plates) across the price and sales matrices; a mismatched order gives wrong products in later parts.

Real-world


  • Representing price lists as matrices lets businesses compute total revenue across many products and outlets in a single matrix multiplication.

Interesting facts

Matrices were introduced as a formal concept by Arthur Cayley in 1858, but the arrangement of data in rectangular arrays goes back to ancient Chinese texts around 200 BCE.

Modern spreadsheet software is essentially a giant matrix, and price-times-quantity revenue calculations are matrix multiplications under the hood.

Question details

Q36 of 44 questions

Board
CBSE
Class
Class 12
Subject
Applied Mathematics
Year
2026
Section
Section E
Marks
1
Chapter
Matrices
Topic
Matrix Representation of Prices
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

Should the price matrix be written as a row or a column?

Either is correct as a standalone answer. However, for the later parts that compute funds by multiplying prices with quantities, choose the orientation that makes the matrices conformable — typically a 1×31 \times 3 row price matrix multiplied by a 3×13 \times 1 column of quantities.

What order should the three prices appear in?

Use the same item order as the sales data — fans, then mats, then plates — so that price 25 aligns with fans, 50 with mats, and 10 with plates when you multiply the matrices.