Show that the definition of linearity in the text is equivalent to the following. If L[y] and

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Show that the definition of linearity in the text is equivalent to the following. If L[y] and L[w] exist, then L[y + w] exists and L[cy] and L[y + w] = L[y] + L[w] as well as L[cy] = cL[y] and L[kw] = kL[w].
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