- #1
eyehategod
- 82
- 0
Find the dimension of the solution space of Ax=0, where
A=1 2 5
-1 3 1
is the rank(A)=2
so the nullity(A)=2?
is this correct?
A=1 2 5
-1 3 1
is the rank(A)=2
so the nullity(A)=2?
is this correct?
The dimension of a solution space refers to the number of independent variables or parameters that are required to describe a solution. It is the minimum number of variables needed to uniquely specify a particular solution.
The dimension of a solution space is determined by the number of equations and variables present in a system. It can be calculated using techniques such as Gaussian elimination or by analyzing the rank of a matrix representing the system of equations.
Yes, a solution space can have a dimension of zero. This means that there are no independent variables or parameters required to describe the solution, and it is a single point or value.
The dimension of a solution space is directly related to the number of solutions. A higher dimension typically means more solutions, while a lower dimension means fewer solutions or even no solutions in some cases.
Yes, the dimension of a solution space can change depending on the system or equations being analyzed. It can also change as more information or constraints are added to the system, which may reduce the number of independent variables needed to describe a solution.