2.10 The following input-output pairs have been observed during the operation of a time-
invariant system:
$x_1(n) = \{1, 0, 2\} \rightarrow y_1(n) = \{0, 1, 2\}$
$x_2(n) = \{0, 0, 3\} \rightarrow y_2(n) = \{0, 1, 0, 2\}$
$x_3(n) = \{0, 0, 0, 1\} \rightarrow y_3(n) = \{1, 2, 1\}$
Can you draw any conclusions regarding the linearity of the system. What is the
impulse response of the system?