Determine if the following statements are true or false Just

Determine if the following statements are true or false. Justify your answers. There is a linear transformation T: F^3 rightarrow F^3 satisfying T(1, 1, 0) = (1, 0, 0), T(0, 1, 1) = (0, 1, 0) and T(1, 0, 1) = (0, 0, 1). There is a linear transformation T: F^3 rightarrow F^3 satisfying T(1, -1, 0) = (1, 0, 0), T(0, 1, -1) = (0, 1, 0) and T(-1, 0, 1) = (0, 0, 1). If T: V rightarrow W is a linear transformation and the list v_1,..., v_n is linearly independent, then the list T(v_1),..., T(v_n) is linearly independent. If T: V rightarrow W is a linear transformation and the list T(v_1),...,T(v_n) is linearly independent, then the list v_1,..., v_n is linearly independent.

Solution

by using theorems , all the above statements are true