Question

If T : V ? R^2 is a linear transformation, and T v = (1, 3), and Tw = (2, 6), find T(2v ? w)

Answer 1

Answer: The required value is (0,0).

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

`T(v)=(1,3)~~~\textup{and}~~~T(w)=(2,6)`

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

Since T is a linear transformation, so we have

`T(av+bw)=aT(v)+bT(w)`, where a, b are scalars and v, w ∈ V.

Therefore, we get

`T(2v-w)\\\\=2T(v)-T(w)\\\\=2(1,3)-(2,6)\\\\=(2,6)-(2,6)\\\\=(2-2,6-6)\\\\=(0,0)`

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