To determine the products of the decomposition reaction of [tex]\(2 \, \text{LiClO}_3\)[/tex], let's analyze the given patterns within the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\multicolumn{1}{|c|}{\text{Reactants}} & \multicolumn{1}{c|}{\text{Products}} \\
\hline
2 \, \text{NaClO}_3 & 2 \, \text{NaCl} + 3 \, \text{O}_2 \\
\hline
2 \, \text{KClO}_3 & 3 \, \text{O}_2 + 2 \, \text{KCl} \\
\hline
2 \, \text{LiClO}_3 & \\
\hline
\end{array}
\][/tex]
By observing the decomposition reactions for sodium chlorate ([tex]\(2 \, \text{NaClO}_3\)[/tex]) and potassium chlorate ([tex]\(2 \, \text{KClO}_3\)[/tex]), we notice a common pattern in the products:
[tex]\[
2 \, \text{MClO}_3 \rightarrow 2 \, \text{MCl} + 3 \, \text{O}_2 \quad \text{where M is a metal}
\][/tex]
Applying this pattern to lithium chlorate ([tex]\(2 \, \text{LiClO}_3\)[/tex]), we expect the products to follow the same form:
[tex]\[
2 \, \text{LiClO}_3 \rightarrow 2 \, \text{LiCl} + 3 \, \text{O}_2
\][/tex]
Thus, the products that Rosa should record in the last row of the table are:
[tex]\[
2 \, \text{LiCl} + 3 \, \text{O}_2
\][/tex]
Therefore, the correct answer for what products to record in the last row of the table is:
[tex]\[ \boxed{2 \, \text{LiCl} + 3 \, \text{O}_2} \][/tex]
