![§1.8 Introduction to Linear Transformations Let A = [a 1 a2 an] be](http://s1.studyres.com/store/data/006151798_1-1596c7f77f21452ed436a495dc65f749-300x300.png)
Sol - Math TAMU
... 4.1 #6. (2 pts.) Prove that the set of nonsingular n×n matrices under the usual operations is not a vector space. Sol. If such collection V is a vector space then V contains a zero vector, i.e., zero matrix 0 of size n × n. However the matrix 0 is singular, and so 0 ∈ / V. This implies that V can no ...
... 4.1 #6. (2 pts.) Prove that the set of nonsingular n×n matrices under the usual operations is not a vector space. Sol. If such collection V is a vector space then V contains a zero vector, i.e., zero matrix 0 of size n × n. However the matrix 0 is singular, and so 0 ∈ / V. This implies that V can no ...
