Correct answer: (B) F=2x+y is such an extension.; (C) There are infinitely many such extensions.
Explanation
Every linear extension is 2x+cy. Its norm on ℓ¹² is max(2,|c|), while ‖f‖=2. Thus exactly coefficients c∈[−2,2] preserve the norm: infinitely many, including c=1 but not c=3. **B,C**.
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