Step 1 :Given the equation: \(\left[\begin{array}{llll}1 & t+2 & 3 & -6\end{array}\right]=3\left[\begin{array}{llll}r & -1 & 1 & -2\end{array}\right]\)
Step 2 :Equating the corresponding elements of the two vectors:
Step 3 :\(1 = 3r\)
Step 4 :\(t + 2 = -3\)
Step 5 :Solving for r and t:
Step 6 :\(r = \frac{1}{3}\)
Step 7 :\(t = -5\)
Step 8 :Final Answer: \(r = \boxed{\frac{1}{3}}\) and \(t = \boxed{-5}\)