BONUS Suppose A is a 3 times 5 matrix and let T be the corre

BONUS: Suppose A is a 3 times 5 matrix, and let T be the corresponding linear transformation. What are the domain and codomain of, T? Is it possible for A to have a null space of just the zero vector? Explain.

Solution

here we have the matrix of T is 3*5 so we have the Transformation T from R^{5 to} R³

domain is R⁵ and codomain is R³

so if you have m by n then we have it to be from Rⁿ to R^m

b. no because if the nullspace of T is just the zero vector then the T transformation must be non singular .but which would imply one to one and onto( theorem from kenneth hoffman linear algebra)

which is not possible here since we have the map frm R^{5 to} R³