Let T be the linear transformation whose standard matrix is

Let T be the linear transformation whose standard matrix is given. Decide if T is a one-to-one mapping. Justify your answer. Choose the correct answer below. The transformation T is not one-to-one because the equation T(x) = 0 has only the trivial solution. The transformation T is not one-to-one because the equation T(x) = 0 has a nontrivial solution. The transformation T is one-to-one because the equation T(x) = 0 has a nontrivial solution. The transformation T is one-to-one because the equation T(x) = 0 has only the trivial solution.

Solution

Answer :

The transformation T is one to one because the equation T(x) = 0 has only trivial solution

Explanation : Let A be the standard matrix of T . Then T is one to one if and only if the equation Ax = b has atmost one solution for each b .