Judgment Questions

1.4

    1. The set {} is a basis for a two-dimensional subspace of . True
    1. The set {} is a basis for a one-dimensional subspace of . True
    1. The set of all vectors of the form is a subspace spanned by the vectors and . True
    1. The set of vectors of the form is a vector in the plane spanned by the vectors and . True
    1. The set {} is a basis for a subspace of . False

1.6

    1. If 𝑆 is a subspace of a vector space 𝑉, then 𝑆 is a vector space. True
    1. It is possible to find a pair of two-dimensional subspaces 𝑆 and 𝑇 of such that 𝑆∩𝑇={𝟎}. False
    1. If 𝑆 and 𝑇 are different proper subspaces of a vector space 𝑉, then 𝑆∪𝑇 is a subspace of 𝑉. False
    1. If 𝑆 and 𝑇 are subspaces of a vector space 𝑉, then 𝑆∩𝑇 is a subspace of 𝑉. True
    1. If span , then they are linearly independent. True
    1. If span a vector space 𝑉, then they are linearly independent. False
    1. If are vectors in vector space 𝑉 and = then are linearly dependent. True
    1. If 𝐴 is an 𝑚×𝑛 matrix, then 𝐴 and have the same rank. True
    1. If 𝐴 is an 𝑚×𝑛 matrix, then 𝐴 and have the same nullity. False
Table Of Contents
Judgment Questions
1.4
1.6