TRUE/FALSE
(a) The set {y(t)| y'+y^2/t=0} is a vector space.
(b) For an invertible matrix M, if M = M^−1, then |M| = 1.
(c) Let A be any 3 × 3 real matrix such that |A| does not equal 0. Then |2A|=2|A|.
(d) If A is an n × n matrix and b ∈ R^n such that Ax = b has no solution, then Ax=c has no solution for any other nonzero vector c∈ R^n
(e) If A is a square matrix and Ax = 0 has a unique solution, then A is invertible.
(f) The set of functions {at^4 + bt + c | a, b, c ∈ R} is a vector space.

Question

TRUE/FALSE  
(a) The set {y(t)| y'+y^2/t=0} is a vector space.
(b) For an invertible matrix M, if M = M^−1, then |M| = 1.
(c) Let A be any 3 × 3 real matrix such that |A| does not equal 0. Then |2A|=2|A|.
(d) If A is an n × n matrix and b ∈ R^n such that Ax = b has no solution, then Ax=c has no solution for any other nonzero vector c∈ R^n
(e) If A is a square matrix and Ax = 0 has a unique solution, then A is invertible.
(f) The set of functions {at^4 + bt + c | a, b, c ∈ R} is a vector space.