<p>I have my final coming up on Tuesday, and I’d like to know why any vectors of the form (a, b, 0) do NOT form a subspace for R3…while vectors of the form (a, 0, 0) do. Thanks a lot.</p>
<p>(I also posted in this is the “Test Prep” forum, but it hasn’t gotten any responses there)</p>
<p>Are you sure they don’t?</p>
<p>We might be using different definitions of subspace - but here’s how I know it:</p>
<p>3 properties must be satisfied - if a,b belong to the subset,</p>
<p>i) 0 belongs to the subset
ii) a+b also belongs to the subset
iii) xa, for any x in R also belongs to the subset</p>
<p>it seems like all three work here.</p>
<p>Yeah, I’ve tested them and it seems to be a subspace, but my linear textbook’s answer key says it’s not…maybe it’s just a mistake then.</p>