Prove that the transformation T: R 2 R 2 defined by T(x, y) = (2x, x + 3y) is linear. Find the image of the vector { 1, 2) under this transformation.

1.1 Systems of Linear Equations Linear equation – equation written in the form “a x +a x +…+a x =b” where 1 1 2 2 n n b & coefficients a 1…,a nre real or complex numbers, usually known in advance System of Linear Equations (linear system) – a collection of one or more linear equations involving the same variables Solution – a list (1 2s ,…,n ) of numbers that makes each equation a true statement when the values s …s 1re nubstituted for x x , r1…pentively Solution set – set of all possible solutions -Equivalent systems have the same solution set A system of linear equations has: 1. No solution (inconsistent system) 2. Exactly one solution (consistent system) 3. Infinitely many solutions (consistent system) Matri