Kunze Linear Algebra · Problem 2.2.1

Vector Spaces

Mathematics — Methods · subspaces-identification

Problem

Which of the following sets of vectors α=(a1,…,an)\alpha = (a_1, \ldots, a_n) in RnR^n are subspaces of RnR^n (n≥3n \geq 3)? (a) all α\alpha such that a1≥0a_1 \geq 0; (b) all α\alpha such that a1+3a2=a3a_1 + 3a_2 = a_3; (c) all α\alpha such that a2=a12a_2 = a_1^2; (d) all α\alpha such that a1a2=0a_1 a_2 = 0; (e) all α\alpha such that a2a_2 is rational.

Browse the problem library