Problem

(a) $\left[\begin{array}{llll}1 & t+2 & 3 & -6\end{array}\right]=3\left[\begin{array}{llll}r & -1 & 1 & -2\end{array}\right]$

Answer

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Answer

Final Answer: \(r = \boxed{\frac{1}{3}}\) and \(t = \boxed{-5}\)

Steps

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 \(t = \boxed{-5}\)

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