Question

Find two linear transformations S:R²→R² and T:R²→R² such that: ST=Z and TS≠Z.

Answer 1

To find linear transformations S and T such that ST=Z and TS≠Z, we can use matrices. For example, S = [1 0; 0 -1] and T = [0 1; 1 0]. ST = Z and TS ≠ Z.

Step-by-step explanation:

In order to find two linear transformations S:R²→R² and T:R²→R² such that ST=Z and TS≠Z, we need to define the transformations in terms of their matrices. Let's consider:

S = [1 0; 0 -1] and T = [0 1; 1 0]

To show that ST=Z, we can multiply the matrices:

ST = [1 0; 0 -1] * [0 1; 1 0] = [0 1; 0 -1] = Z

To show that TS≠Z, we can multiply the matrices:

TS = [0 1; 1 0] * [1 0; 0 -1] = [0 -1; 1 0] ≠ Z