Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Vector Spaces
Which of the following sets of functions from ℝ to ℝ is a vector space over ℝ?
\(S_{1}=\left\{f \mid \lim _{x \rightarrow 3} f(x)=0\right\}\)
\(S_{2}=\left\{g \mid \lim _{x \rightarrow 3} g(x)=1\right\}\)
\(S_{3}=\left\{h \mid \lim _{x \rightarrow 3} h(x) \text { exists }\right\}\)
1
Only S1
2
Only S2
3
S1 and S3 but not S2
4
All the three are vector spaces