- #1
lacrotix
- 9
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HI there. I'm taking Linear Algebra classes right now and this question has been bugging me.
Find a general solution to the system, state the dimension of the solution space, and confirm the row vectors of A are orthogonal to the solution vectors.
The given system is:
(x1) + (x2) + (x3) = 0
2(x1) + 2(x2) + 2(x3) = 0
3(x1) + 3(x2) + 3(x3) = 0
This last part about confirming vectors are orthogonal (bolded) confuses me. I have found the general solution can be written as
(x1) = t + s
(x2) = t
(x3) = s
And that the dimension of the solution is 2, since there are two vectors. But I do not understand how to do the last part of the question. What is it asking? Any guidance would be appreciated.
Homework Statement
Find a general solution to the system, state the dimension of the solution space, and confirm the row vectors of A are orthogonal to the solution vectors.
The given system is:
(x1) + (x2) + (x3) = 0
2(x1) + 2(x2) + 2(x3) = 0
3(x1) + 3(x2) + 3(x3) = 0
The Attempt at a Solution
This last part about confirming vectors are orthogonal (bolded) confuses me. I have found the general solution can be written as
(x1) = t + s
(x2) = t
(x3) = s
And that the dimension of the solution is 2, since there are two vectors. But I do not understand how to do the last part of the question. What is it asking? Any guidance would be appreciated.