Answer: The required value is (0,0).
Step-by-step explanation: Given that T : V ---> R² is a linear transformation and
[tex]T(v)=(1,3)~~~\textup{and}~~~T(w)=(2,6)[/tex]
We are given to find the value of T(2v - w).
Since T is a linear transformation, so we have
[tex]T(av+bw)=aT(v)+bT(w)[/tex], where a, b are scalars and v, w ∈ V.
Therefore, we get
[tex]T(2v-w)\\\\=2T(v)-T(w)\\\\=2(1,3)-(2,6)\\\\=(2,6)-(2,6)\\\\=(2-2,6-6)\\\\=(0,0)[/tex]
Thus, the required value is (0, 0).
