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
- The variance of the following probability distribution is:
\[ \begin{array}{|c|c|} \hline x & P(X) \\ \hline 0 & \frac{9}{16} \\ 1 & \frac{3}{8} \\ 2 & \frac{1}{16} \\ \hline \end{array} \]- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- The negative of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
- The converse of \( ((\sim p) \land q) \Rightarrow r \) is:
- MHT CET - 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
- If \[ B = \begin{bmatrix} 3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \] is the adjoint of a 3x3 matrix \( A \) and \( |A| = 4 \), then \( \alpha \) is equal to:
- MHT CET - 2024
- Mathematics
- Transpose of a Matrix
Questions Asked in JEE Main exam
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Waves and Oscillations
- A complex number 'z' satisfy both \(|z-6|=5\) & \(|z+2-6i|=5\) simultaneously. Find the value of \(z^3 + 3z^2 - 15z + 141\).
- JEE Main - 2026
- Algebra
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
- JEE Main - 2026
- Rotational motion
- If \[ \frac{\tan(A-B)}{\tan A}+\frac{\sin^2 C}{\sin^2 A}=1, \quad A,B,C\in\left(0,\frac{\pi}{2}\right), \] then:
- JEE Main - 2026
- Trigonometry
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.”