Find a basis of R^3 defined by the equation,
I took the above equation and solved for x3, assuming that was saying that x3 could be created using -2 copies of x1 minus 3 copies of x2...
Then I solved this like I solve for a kernel.
Which gave me a result of,
However, the answer is:
Where did I go wrong? Any help is extremely appreciated. Thanks!
Also note that the problem should be "Find a basis of the subspace of R^3 defined by the equation,
Since that is one equation constraining the three variables, the subspace has dimension 3- 1= 2 and so your basis should contain 2 vectors, just as you say.