Recent questions tagged goclasses-cs-dpp-day-242

For which vector(s) $b$ below does the system $ \begin{bmatrix}1 & 2 \\3 & 5 \\2 & 3\end{bmatrix} x = b $ have a solution?$ \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} $ $ ...

Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknow...

Let $$S=\left \{ x \in\mathbb{R} \mid x=\operatorname{Trace}(A) \text{ for some } A \in M_{4} (\mathbb{R}) \text{ such that }A^{2}=A \right\}.$$Then which of the followi...

Let $A$ be an $n \times n$ matrix with rank $k$. Consider the following statements:If $A$ has real entries, then $AA^{t}$ necessarily has rank $k$If $A$ has complex entri...

Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is:$D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist.

Let $R=\{(1,3),(4,2),(2,4),(2,3)$, $(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ isa function.transitive.not symmetric.reflexive.

Let $R=\{(3,3),(6,6),(9,9),(12,12)$, $(6,12),(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$. The relation isreflexive and symmetric only.an equivalence r...

Let $W$ denotes the words in the English dictionary define the relation $R$ by $R=\{(x, y) \in W \times W$ : the words $x$ and $y$ have atleast one letter in common$\}$. ...

Let $R$ be the real line. Consider the following subsets of the plane $R \times R$$S=\{(x, y): y=x+1 \text { and } 0<x<2\}$$T=\{(x, y): x-y$ is an integer $\}$Which one o...

Consider the following relations$R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\} $;$S=\left\{\left.\left(\frac{m}{n}, \frac{p}{q}\right) ...