B

9000019808

Level: 
B
Assuming \(x\in \mathbb{C}\), find the solution set of the following equation. \[ x\left (x + 1\right )\left (x^{2} + 1\right ) = 0 \]
\(\left \{-1;0;-\mathrm{i};\mathrm{i}\right \}\)
\(\left \{-1;0;1;-\mathrm{i};\mathrm{i}\right \}\)
\(\left \{-1;1;-\mathrm{i};\mathrm{i}\right \}\)
\(\left \{-1;0;-\mathrm{i}\right \}\)

9000019809

Level: 
B
Find the factorization of the following equation. \[ x^{3} + 3x^{2} - x - 3 = 0 \]
\(\left (x + 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x - 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x + 1\right ) = 0\)

9000019904

Level: 
B
The coefficient matrix of a \(3\times 3\) linear system is \(A\) and the augmented matrix \(A'\). Find \(\mathop{\mathrm{rank}}(A)\) and \(\mathop{\mathrm{rank}}(A')\). \[ A = \begin{pmatrix} -1 & 3 & 2 \\ 0 & 4 & -5 \\ 0 & 0 & 2 \end{pmatrix} \qquad A' = \left(\begin{array}{ccc|c} -1 & 3 & 2 & 5 \\ 0 & 4 & -5 & 10\\ 0 & 0 & 2 & 0 \end{array}\right) \]
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 2\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 2\)