To evaluate the expression [tex]\(5(1,3) - 3(2,-1)\)[/tex], follow these detailed steps:
1. Scale the first vector: Multiply the vector [tex]\((1,3)\)[/tex] by 5.
[tex]\[
5(1,3) = (5 \cdot 1, 5 \cdot 3) = (5, 15)
\][/tex]
2. Scale the second vector: Multiply the vector [tex]\((2,-1)\)[/tex] by -3.
[tex]\[
-3(2,-1) = (-3 \cdot 2, -3 \cdot -1) = (-6, 3)
\][/tex]
3. Add the scaled vectors: Add the results of the scaled vectors from steps 1 and 2.
[tex]\[
(5, 15) + (-6, 3) = (5 + (-6), 15 + 3) = (-1, 18)
\][/tex]
Therefore, the evaluated expression [tex]\(5(1,3) - 3(2,-1)\)[/tex] is [tex]\((-1, 18)\)[/tex].
So, the answer is:
D. [tex]\((-1, 18)\)[/tex]
