Math Problem Statement

A table presents sales data for three products (11 - A, 11 - B, 11 - C) over three days (1st, 2nd, 3rd), divided into two price categories (Rs. 50 and Rs. 100). The problem requires calculating matrices (M, P, R) based on daily data, finding their average, and solving a matrix multiplication problem involving a vector K.

Solution

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Table:

The table presents sales data for three products (11 - A, 11 - B, 11 - C) over three days (1, 2, 3). The data is divided into two price categories (Rs. 50 and Rs. 100) for each day.

1st Day2nd Day3rd Day
Rs. 50Rs. 100Rs. 50Rs. 100Rs. 50Rs. 100
11 - A207516801240
11 - B126015751845
11 - C098024902470

Questions:

i. Calculate matrix MM using the first day's data.
ii. Calculate matrix PP using the second day's data.
iii. Calculate matrix RR using the third day's data.
iv. Find 13(M+P+R)\frac{1}{3}(M + P + R).
v. If K=[2030]K = \begin{bmatrix} 20 \\ 30 \end{bmatrix} and A=RKA = RK, calculate AA.

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Math Problem Analysis

Mathematical Concepts

Matrix Operations
Averaging Matrices
Matrix Multiplication

Formulas

Matrix addition: \( M + P + R \)
Averaging: \( \frac{1}{3}(M + P + R) \)
Matrix multiplication: \( A = RK \)

Theorems

-

Suitable Grade Level

Grades 10-12