Recent questions tagged goclasses-cs-dpp-day-246

Let $A$ be an $m \times n$ matrix, $B$ be an $n \times m$ matrix, and $C$ be an $m \times m$ matrix. Which of the following statement(s) is(are) true?$\operatorname{tr}(A...

Let $A=\begin{bmatrix}2&-1&3\\4&2&11\\-2&13&10\end{bmatrix}$. In the $LU$ decomposition $A=LU$, where $L$ is unit lower triangular and $U$ is upper triangular, the matrix...

The eigenvalues of a $3 \times 3$ matrix $A$ are $-2$, $4$, and $5$. Then the trace of the matrix $A^3-2A^2+3A$ is:$93$ $99$ $112$ $117$

Which one of the following statements is NOT always true for a real square matrix $A$?If $A$ is diagonalizable and all eigenvalues of $A$ are equal to $2$, then $A=2I$. I...

The determinant of the matrix $A=\begin{bmatrix} 1&1&1&1 \\ p&q&r&s \\ p^2&q^2&r^2&s^2 \\ p^3&q^3&r^3&s^3 \end{bmatrix}$ is  $(q-p)(r-p)(s-p)(r-q)(s-q)(s-r)$ $(q-p)(r-p)(...

What is the identity element of the group of non-zero real numbers under multiplication?01-110

Which of the following sets with the given operation is a group?The set of all integers with addition.The set of all natural numbers with multiplication.The set of all ra...

Which of the following is an example of a group$(R,-)$$(Z,-)$$(R,+)$$(Q,-)$

Which of the following is an abelian group?The group of all permutations of a set.The group of all $\mathbf{2} \times \mathbf{2}$ invertible matrices.The group of all rot...

If $G$ is a group and $g \in G$, the order of $g$ is defined as:The smallest positive integer $n$ such that $g^n=e$.The largest positive integer $n$ such that $g^n=e$.The...