Solve the Problem A) $\operatorname { dim } \operatorname { Nul } \mathrm { A } = 5 , \operatorname { dim } \operatorname { Col } \mathrm { A } = 2$

Solve the problem.
- $$A = \left[ \begin{array} { r r r r r c r } 1 & - 2 & 3 & 1 & 0 & 5 & - 4 \\0 & 0 & 1 & - 6 & 2 & - 2 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 3 \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{array} \right]$$

A) $\operatorname { dim } \operatorname { Nul } \mathrm { A } = 5 , \operatorname { dim } \operatorname { Col } \mathrm { A } = 2$
B) $\operatorname { dim } \operatorname { Nul } \mathrm { A } = 3 , \operatorname { dim } \operatorname { Col } \mathrm { A } = 4$
C) $\operatorname { dim } \operatorname { Nul } \mathrm { A } = 4 , \operatorname { dim } \operatorname { Col } \mathrm { A } = 3$
D) $\operatorname { dim } N u l A = 2 , \operatorname { dim } \operatorname { Col } A = 5$