Recent questions tagged goclasses-cs-dpp-day-236

Let $$ A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix} \text{ and } B=\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}.$$ Thenther...

Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by$$\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha ...

The values of $a$ for which the following system of equations$$\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & a \\ x & + & 4y & + & 10z & = & a ^...

Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix$$A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & – \sin t & \cos t \end{bmatrix}.$$...

Let $A_{ij}$ denote the minors of an $n \times n$ matrix $A$. What is the relationship between $\mid A_{ij} \mid $ and $\mid A_{ji} \mid $?They are always equal $\mid A_{...

Let $A$ and $B$ be two sets such that $|A|=m$ and $|B|=n$. The number of elements in power set of $A \times B$ is$2^{m+n}$$2^{m n}$$2^{m^n}$$2^{n^m}$

Let $\mathcal{R}$ be a relation on natural numbers defined as $\mathcal{R}=\left\{\left(n, n^2\right) \mid n \in \mathbb{N}\right\}$. Then $\mathcal{R}$ isReflexiveTransi...

Let A be a set with $n$ elements. Let $a, b \in A$, be two distinct elements. Then the total number of relations on A that contain $(a, b)$ is$2^{n^2}-1$$2^{n-1}$$2^{n^2-...

The empty relation on set $X=\{a, b, c\}$ is:Neither reflexive nor symmetricSymmetric and reflexiveTransitive and reflexiveTransitive and symmetric

Let $A$ be a set with cardinality $n$. There are total 1024 symmetric relations on $A$. Then value of n is36104