Question

Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample. (10) i) 2 has innitely many non-zero, proper vector subspaces. ii) If ∶ → is a one-one linear transformation between two nite dimensional vector spaces and then is invertible. iii) If = 0 for a square matrix , then all the eigenvalues of are zero. iv) Every unitary operator is invertible. v) Every system of homogeneous linear equations has a non-zero solution.

Answer 1

Answer:

second is write because that is answeravam