If t : v ? r^2 is a linear transformation, and t v = (1, 3), and tw = (2, 6), find t(2v ? w)

 The required value is (0,0).

Step-by-step explanation:  Given that T : V ---> R² is a linear transformation and

We are given to find the value of T(2v - w).

Since T is a linear transformation, so we have

, where a, b are scalars and v, w ∈ V.

Therefore, we get

Thus, the required value is (0, 0).

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.