If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
We know that if a matrix is of the order m × n, it has mn elements.
Thus, to find all the possible orders of a matrix having 24 elements,
we have to find all the ordered pairs of natural numbers whose product is 24.
The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and (6, 4)
Hence, the possible orders of a matrix having 24 elements are:
1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, and 6 × 4 (1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13.
Hence, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).
Balance Sheet of Atharv and Anmol as at 31st March, 2024
Liabilities | Amount (₹) | Assets | Amount (₹) |
---|---|---|---|
Capitals: | Fixed Assets | 14,00,000 | |
Atharv | 8,00,000 | Stock | 4,90,000 |
Anmol | 4,00,000 | Debtors | 5,60,000 |
General Reserve | 3,50,000 | Cash | 10,000 |
Creditors | 9,10,000 | ||
Total | 24,60,000 | Total | 24,60,000 |
Column-I | Column-II |
---|---|
(a) Non-tax Revenue | (ii) Free-rider |
(b) Indirect Tax | (i) Goods and Services Tax |
(c) Capital expenditure | (iii) Borrowings |
(d) Private goods | (iv) Rivalrous in nature |
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.