matrix

Let $M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}$ be a $2 \times 2$ matrix, where $\theta = \frac{2\pi}{5}$, and $I_2 = \begin{pmatrix...

Let $\gamma_1, \gamma_2, \gamma_3$ be the eigenvalues of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}$, where $t \in [-\pi, \p...

Let M = (I_n - (1/n)11^T) be a matrix, where 1 = (1,1,1, ...,1)^T ∈ R^n and I_n is the identity matrix of order n. Which of the following options is/are correct?

Let A$_{5 \times 5}$ be a matrix such that each of its elements follows Bernoulli(p = 0.50) distribution independently. The probability that the row-sum of the second row and the c...