We were said at school that the language $L$ over an alphabet $\sum = \{a,b\}$ where the number of $a$'s is twice the number of $b$'s, formally $L = \{ w \in \{a,b\}^* \mid |w|_a = 2|w|_b \}$ cannot be generated by linear grammar. I was wondering, is there a way to prove it, to make it clear why is that so? I was thinking about applying the pumping lemma might work, but I wasn't succesful proving it.
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