# Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 20/Solution 1

Jump to: navigation, search

The set of solutions to the homogeneous system has ${\displaystyle 2}$ parameters, so the dimension of the null space of this matrix is ${\displaystyle 2}$.

The dimension of the domain is ${\displaystyle 4}$. By the Rank-Nullity Theorem, we have ${\displaystyle \mathrm {rank} (A)+\mathrm {null} (A)=4}$.

Thus, the rank of ${\displaystyle A}$ is ${\displaystyle \color {blue}2}$.