Verify that 1k, (-2k), 3k are linearly independent signals. | Mathematics II 2078

Mathematics II20785 marksNumerical: linear independence of signalsApplications to difference equations

Verify that $1k$ , $(-2^k)$ , $3k$ are linearly independent signals. [5]

Verify that $1k$, $(-2^k)$, $3k$ are linearly independent signals. [5]

Three signals to test for linear independence: $f1(k) = 1^k, \quad f2(k) = (-2)^k, \quad f3(k) = 3^k$ No other numeric data required. --- Signals $\{f1, f2, f3\}$ are linearly independent if $C1 f1(k) + C2 f2(k) + C3 f3(k) = 0 \quad \text{for all } k$ implies $C1 = C2 = C3 = 0$ . $$C1 (1)^k + ...

Three signals to test for linear independence: $$f1(k) = 1^k, \quad f2(k) = (-2)^k, \quad f3(k) = 3^k$$ No other numeric data required. --- Signals ${f1, f2, f3}$ are linearly independent if $$C1 f1(k) + C2 f2(k) + C3 f3(k) = 0 \quad \text{for all } k$$ implies $C1 = C2 = C3 = 0$. $$C1 (1)^k + ...

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