B

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 \(\mathop{\mathrm{rank}}(A')\). \[ A = \begin{pmatrix} -1 & 3 & 2 \\ 0 & 4 & -5 \\ 0 & 0 & 2 \end{pmatrix} \qquad A' = \left(\begin{array}{ccc|c} -1 & 3 & 2 & 5 \\ 0 & 4 & -5 & 10\\ 0 & 0 & 2 & 0 \end{array}\right) \]
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 2\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 2\)

9000014201

Level: 
B
Find intersection points of the graph of the rational function \( f(x) = \frac{2x - 3} {x - 2} \) with \(y\)-axis.
\(Y = \left [0, \frac{3} {2}\right ]\)
\(Y = \left [\frac{3} {2},0\right ]\)
\(Y _{1} = \left [0, \frac{3} {2}\right ]\text{ and }Y _{2} = \left [\frac{3} {2},0\right ]\)
\(Y = \left [2,2\right ]\)