Thread: Problem finding a basis for a given subspace

Ok, so I need to find a basis for subspace A.

A = {(x1, x2, x3) E R^3 | 2x1 + x3 = 0, x1 + x2 - x3 = 0} of R^3

I understand how to determine whether something is a basis of something else, but I cannot wrap my head around how to determine my own basis for this subspace.

Originally Posted by crymorenoobs

Ok, so I need to find a basis for subspace A.

A = {(x1, x2, x3) E R^3 | 2x1 + x3 = 0, x1 + x2 - x3 = 0} of R^3

I understand how to determine whether something is a basis of something else, but I cannot wrap my head around how to determine my own basis for this subspace.

Set then you have a system of two equations in two unknowns.

Using the first equation you get



Using the 2nd equation we get


Using this we get



So any multiple of the last vector will space that space.