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# Simultaneous equation help watch

1. When writing my maths notes and doing the questions, I'm stumped on the following simulatenous equations:

I know that and , but I'm not sure how to find the values. Any help would be appreciated
2. (Original post by SecretDuck)
When writing my maths notes and doing the questions, I'm stumped on the following simulatenous equations:

I know that and , but I'm not sure how to find the values. Any help would be appreciated
What you have is a system of two equations in three variables. That means it's underdetermined: the solutions, if they exist, are not unique. You've reduced them to their simplest form, such that given , you can produce a solution ; that's the best you can do.

That is to say, the solution to the system is precisely .
3. (Original post by Smaug123)
What you have is a system of two equations in three variables. That means it's underdetermined: the solutions, if they exist, are not unique. You've reduced them to their simplest form, such that given , you can produce a solution ; that's the best you can do.

That is to say, the solution to the system is precisely .
Oh right, it's just the lecturer came up with the answers:
a=1, b=1 and c=-2
4. (Original post by SecretDuck)
Oh right, it's just the lecturer came up with the answers:
a=1, b=1 and c=-2
(1,1,-2) is indeed a solution; indeed, in , the set of solutions is precisely those elements on the line spanned by the vector .
5. (Original post by Smaug123)
(1,1,-2) is indeed a solution; indeed, in , the set of solutions is precisely those elements on the line spanned by the vector .
Yes, the answer is supposed to be an orthogonal complement to a matrix. Thank you

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