Recent questions tagged goclasses-cs-dpp-day-244

Let $P$ be a $3 \times 3$ real matrix such that $P^3-6P^2+11P-6I=0$ and $\operatorname{tr}(P)=7$. Then $\det(P)=$$8$ $10$ $12$ $18$

Consider the matrix $A=\begin{bmatrix}4&1&0&0&1\\1&4&1&0&0\\0&1&4&1&0\\0&0&1&4&1\\1&0&0&1&4\end{bmatrix}$.The largest eigenvalue of $A$ is ______.

Suppose that $Q$ is a $6\times 8$ matrix such that every solution of the equation $Qx=0$ is of the form $x=s(1,0,-1,2,0,3,1,-2)^T+t(0,1,2,-1,1,0,4,3)^T+u(2,-1,0,1,3,-2,0,...

Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$Add the third row to the second row Subtract the t...

What values of $x, y$ and $z$ satisfy the following system of linear equations?$$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \en...

If $f: \mathbb{Z} \rightarrow \mathbb{Z}$ is defined as $f(n)=11 n$ and $g: \mathbb{Z} \rightarrow \mathbb{Z}$ is defined as $g(n)=(n) \bmod 7$, then $(g \circ f)(4)$ is:...

A function $f$ is ______ , if and only if, each element in the co-domain of $f$ is the image of atmost one element in the domain. Fill the blank space:Neither one-one nor...

Let $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(n)=n+15$. Then $f$ isBijectiveOne-oneOntof is not a function

Let $X=\{1,2,3\}$. If $f: X \rightarrow X$ be defined as $f(1)=3, f(2)=1$, and $f(3)=2$, then $f(f(1))$ is:123Not defined

Let $A$ be a set with cardinality $n$. There are total 720 one-one functions from $A$ to $A$. Then value of $n$ is36104