Question:
If a matrix has 36 elements, the number of possible orders it can have is:
If a matrix has 36 elements, the number of possible orders it can have is:
Show Hint
The number of possible orders of a matrix with \( n \) elements is equal to the number of factor pairs of \( n \). Each pair \( (m, n) \) represents a valid order where \( m \times n = n \).
Updated On: Mar 6, 2025
- 13
- 3
- 5
- 9
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The total number of elements in a matrix is given by the product of its number of rows and columns:
\[
m \times n = 36,
\]
where \( m \) is the number of rows, and \( n \) is the number of columns.
To determine the possible orders of the matrix, find all pairs of positive integers \( (m, n) \) such that their product equals \( 36 \). These pairs are the factors of \( 36 \):
\[
(1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), (18, 2), (36, 1).
\]
There are \( 9 \) such pairs, corresponding to \( 9 \) possible orders of the matrix.
Hence, the number of possible orders is (D) 9.
Was this answer helpful?
1
0
Top Questions on Matrix
- If \( A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix} \), then find the value of \( K \) if \( A^2 = 6A + K I_2 \), where \( I_2 \) is the identity matrix.
- Let \( A \) be a square matrix of order 3 such that \( \text{det}(A) = -2 \) and \( \text{det}(3 \cdot \text{adj}(-6 \cdot \text{adj}(3A))) = 2^{m+n} \cdot 3^{mn} \), where \( m > n \). Then \( 4m + 2n \) is equal to:
- Let \( A \) be a \( 3 \times 3 \) matrix such that \( X^T AX = 0 \) for all nonzero \( 3 \times 1 \) matrices \( X = \begin{pmatrix} x \\ y \\ z \end{pmatrix} \). \[ A = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \quad A = \begin{bmatrix} 1 \\ 4 \\ -5 \end{bmatrix}, \quad A = \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix}, \quad A = \begin{bmatrix} 0 \\ 4 \\ -8 \end{bmatrix} \] If \( \det(\text{adj}(2(A + I))) = 2^{\alpha} 3^{\beta} 5^{\gamma} \), \( \alpha, \beta, \gamma \in \mathbb{N} \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is:
Let $ A = \begin{bmatrix} 2 & 2 + p & 2 + p + q \\4 & 6 + 2p & 8 + 3p + 2q \\6 & 12 + 3p & 20 + 6p + 3q \end{bmatrix} $ If $ \text{det}(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n, \, m, n \in \mathbb{N}, $ then $ m + n $ is equal to:
- Three students run on a racing track such that their speeds add up to 6 km/h. However, double the speed of the third runner added to the speed of the first results in 7 km/h. If thrice the speed of the first runner is added to the original speeds of the other two, the result is 12 km/h. Using the matrix method, find the original speed of each runner.
View More Questions
Questions Asked in CBSE CLASS XII exam
- Find the shortest distance between the lines: \[ \frac{x+1}{2} = \frac{y-1}{1} = \frac{z-9}{-3} \] and \[ \frac{x-3}{2} = \frac{y+15}{-7} = \frac{z-9}{5}. \]
- Ajay Ltd. forfeited 100 shares of Rs 10 each for non-payment of first call of Rs 1 per share and second and final call of Rs 3 per share. The minimum price per share at which these shares can be reissued will be:
- Piyush, Aadi and Sudha were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 3. Aadi died on 1st October, 2024. As per the partnership deed, Aadi’s share of profit or loss till the date of death was to be calculated on the basis of sales. Sales for the year ended 31st March, 2024 amounted to ₹ 6,00,000 and that from 1st April to 30th September, 2024 amounted to ₹ 2,00,000. The profit for the year ending 31st March, 2024 was calculated as ₹ 1,50,000. The books of accounts are closed on 31st March every year. Calculate Aadi’s share of profits in the firm and pass necessary journal entries for the same. Show your working clearly.}
- CBSE CLASS XII - 2025
- Retirement and Death of a Partner
- In the figure, curved lines represent equipotential surfaces. A charge \( Q \) is moved along different paths A, B, C, and D. The work done on the charge will be maximum along the path:
- CBSE CLASS XII - 2025
- Electrostatics
- The following information has been extracted from the books of Ram Lal Ltd.:
Comparative Financial Data as on 31st March, 2024 and 2023
Additional Information: Interim dividend paid during the year was \textrupee{ 1,20,000}.Particulars 31.03.2024 (₹) 31.03.2023 (₹) Surplus (P&L) 17,00,000 8,00,000 Patents -- 50,000 Sundry Debtors 5,80,000 4,20,000 Sundry Creditors 1,40,000 60,000 Cash and Cash Equivalents 2,00,000 90,000 - CBSE CLASS XII - 2025
- Cash Flow Statement
View More Questions