Recent questions tagged goclasses-da-dpp-day-135

Let $X$ be a square matrix. Consider the following two statements on $X$.$X$ is invertible. Determinant of $X$ is non-zero. Which one of the following is TRUE?I implies I...

The nullity of $A=\begin{pmatrix}2&3&7\\1&1&9\\9&2&x\end{pmatrix}$ is $1$, then the value of $x$ is $\_\_\_\_\_\_\_\_\_\_\_$.

Let $A$ be a $2 \times 2$ matrix with integer entries. Which of the following could be its eigenvalue?$\sqrt[3]{2}$ $\pi$ $\dfrac{1}{\sqrt{2}}$ $\sqrt{2}$

If $s=a+b+c$, then the value of $\Delta=\begin{vmatrix} s+c & a & b \\ c & s+a & b \\ c & a & s+b \end{vmatrix}$$2s^2$ $2s^3$ $s^3$ $3s^3$

Consider the matrix $A=\begin{pmatrix} 1 & 2 & 0\\ 3 & c & 1\\ 0 & 1 & 1 \end{pmatrix}$. For which value of $c$ is the factorization $A=LU$ impossible? $4$  $5$  $6$  $8$