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