Let A = [aij] be a square matrix of order 3 such that aij = 2j–i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + … + A10 is equal to
- \((\frac{3^{10}-3}{2})A\)
- \((\frac{3^{10}-1}{2})A\)
- \((\frac{3^{10}+1}{2})A\)
- \((\frac{3^{10}+3}{2})A\)
The Correct Option is A
Solution and Explanation
The correct option is(A): \((\frac{3^{10}-3}{2})A\)
A3 = A.A2 = A(3A) = 3A2 = 32A
A4 = 33A
Now
A2 + A3 + … + A10
A[31 + 32 + 33 + … + 39]
\((\frac{3^{10}-3}{2})A\)
Top Questions on Transpose of a Matrix
If the matrix $ A $ is such that $ A \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix} = \begin{pmatrix} -4 & 1 \\ 7 & 7 \end{pmatrix} \text{ then } A \text{ is equal to} $
- COMEDK UGET - 2024
- Mathematics
- Transpose of a Matrix
If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} \quad \text{and} \quad A \, \text{adj} \, A = A A^t, \quad \text{then} \, 5a + b \, \text{is equal to}$
- COMEDK UGET - 2024
- Mathematics
- Transpose of a Matrix
If $3A + 4B^{t} = \left( \begin{array}{cc} 7 & -10 \\ 0 & 6 \end{array} \right) $ and $ 2B - 3A^{t} = \left( \begin{array}{cc} -1 & 18 \\ 4 & -6 \\ -5 & -7 \end{array} \right) $, then find $ (5B)^{t}$:
- COMEDK UGET - 2024
- Mathematics
- Transpose of a Matrix
- If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- The inverse of the matrix \[ \begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 3 \\ 5 & 2 & -1 \end{bmatrix} \] is:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
Questions Asked in JEE Main exam
- The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of \( ABC \) is:
- JEE Main - 2025
- Thermodynamics terms
- The greatest value of \( n \), where \( n \in \mathbb{N} \), such that \( 3^n \) divides \( 50! \) is:
- JEE Main - 2025
- Number Systems
Match List-I with List-II.
Choose the correct answer from the options given below :- JEE Main - 2025
- Thermodynamics
- Let \( y = f(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that \( f(0) = 0 \). If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then \( \alpha^2 \) is equal to __________.
- JEE Main - 2025
- Differential equations
- Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:
- JEE Main - 2025
- Statistics
Concepts Used:
Matrix Transformation
The numbers or functions that are kept in a matrix are termed the elements or the entries of the matrix.
Transpose Matrix:
The matrix acquired by interchanging the rows and columns of the parent matrix is termed the Transpose matrix. The definition of a transpose matrix goes as follows - “A Matrix which is devised by turning all the rows of a given matrix into columns and vice-versa.”