4. Suppose V is finite-dimensional and S, T are linear operators on V. Prove that ST = I if and only if T'S = I. Hint: You can use the result from the previous question.

7. Suppose that T : R² → R² is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is T one-to-one?

3. In M3x2(F), prove that the set { ( ) ( ) ( ) ( ) ( ) } " 0 0 1 is linearly dependent.

Suppose S = {r, u, d) is a set of linearly independent vectors. If z = 2r + 4u + 2d, determine whether T = {r, u, z} is a linearly independent set. Select an Answer 1. Is T linearly independent or dependent? If T is dependent, enter a non-trivial linear relation below. Otherwise, enter 0's for the coefficients. r+ u+ z = 0.

I need to solve the question (5.79) (b)