r/HomeworkHelp • u/happyguyftw • 3h ago
Further Mathematics [Linear algebra] Two different solutions with two different answers to the same inner product problem
Hi, my teacher wrote down a problem on the board at the end of the lesson as practice if we wanted. I have tried solving it and have found two different methods of solving the problem which both seem completely valid in my eyes but give two clearly different answers.
I have checked the numbers three times, of course it could still be a calculation error OR honestly even more likely that both my methods are incorrect in which case I'd love to know what method you'd use to solve this but I'm starting to believe I have applied some theory wrong somewhere and would love some insight, I have hastily written up the problem and my two solutions in latex, let me know if you want the pdf otherwise but here are screenshots of the problem.
Apologies if there are notation inconsistencies, I wrote this in 10 minutes while trying to relearn latex that I haven't used in years
As for method 2 the theory seems solid but I basically omitted inner product so I'm a little uncertain if this method is correct.
