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Solve the following.
In a market survey, three commodities A, B and C were studied. Each commodity had three varieties…
In a market survey, three commodities A, B and C were studied. Each commodity had three varieties. To find out the index number of A, B and C fixed weights were assigned to the three varieties of each of the commodities.
The table given below shows the result of the survey.
Represent the above information in a matrix form.
| Commodity / Variety | I | II | III | Total weight |
|---|---|---|---|---|
| A | 1 | 2 | 3 | P |
| B | 2 | 4 | 5 | Q |
| C | 3 | 5 | 6 | R |
Answer
Answer
AIWriting the weights of the three varieties (columns I, II, III) for A, B and C as the rows of a matrix:
$W = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix}, \qquad \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix}\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} P \\ Q \\ R \end{pmatrix}$
Final answer: $\begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix}$
From ISC 2025 Improvement Mathematics Paper 1, question 6(i).