Quiz Chapter 04: Unary Operations

1. If the determinant of a $4 \times 4$ matrix $\left[ A \right]$ is given as $20$, then the determinant of $5 \left[ A \right]$ is

2. If the matrix product $\left[ A \right] \left[ B \right] \left[ C \right]$ is defined, then $\left( \left[ A \right] \left[ B \right] \left[ C \right] \right)^{T}$ is

3. The trace of a matrix $\begin{bmatrix} 5&6&-6 \\ 9&-11&13 \\ -17&19&23 \\ \end{bmatrix}$ is

4. A square $n \times n$ matrix $\left[ A \right]$ is symmetric if

5. The determinant of the matrix $\begin{bmatrix} 25&5&1 \\ 0&3&8 \\ 0&9&a \\ \end{bmatrix}$ is 50. The value of $a$ is then

6. $\left[ A \right]$ is a $5 \times 5$ matrix and a matrix $\left[ B \right]$ is obtained by the row operations of replacing Row $1$ with Row $3$, and then Row $3$ is replaced by a linear combination of $2 \times$ Row $3+4 \times$ Row $2$. If det$\left( A \right) = 17$, then det$\left( B \right)$ is equal to