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please provide detailed solution for a to c, thank you

3. Consider two state vectors in a Hilbert space given by |v) = A [i|01) + 3i|02) -|03)], |x) = B [|01) – i|02) + 51|03)] : - (b 390 (a) Find the constants A and B such that the state vectors are normalized. Are the two vectors linearly independent? Prove your answer. (c) Let | = |+|x). Calculate the inner product (0|0).
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Transcribed Image Text:3. Consider two state vectors in a Hilbert space given by |v) = A [i|01) + 3i|02) -|03)], |x) = B [|01) – i|02) + 51|03)] : - (b 390 (a) Find the constants A and B such that the state vectors are normalized. Are the two vectors linearly independent? Prove your answer. (c) Let | = |+|x). Calculate the inner product (0|0).
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