Helping you choose a journal is exactly the sort of aid your advisor should be giving you. Often in the relationship between an advisor and a graduate student there is a lack of clarity and/or a miscommunication about what the student should be doing on his own and what his advisor could be helping him out with. I remember that one of my students gave as part of an oral exam a talk on an important paper. He asked me about it a little bit, but not as much as I was expecting. When he gave the talk it was excellent, except that at one point he presented a sort of black box and said "unfortunately I didn't understand this". It was (to me) no big deal, but I had to wonder, "If you understood everything except this one thing, why didn't you ask me about that thing before the exam?" He must have had different ideas about the amount of independence that was being asked of him.
The point of the above story is this: given what little you've said, I am not yet persuaded that your advisor is unwilling to help you choose a journal for your paper: why wouldn't he be willing to help? In general, here is a good strategy for getting help from any faculty member: rather than saying "I'm stumped; please advise," try something and then get feedback on the merits of what you tried. In your case you have the idea of submitting to Linear Algebra and its Applications because you answer some open questions raised in a previous paper in that journal. To me that sounds like an excellent idea: I have several times submitted to journals with the same idea (unfortunately, acknowledging that you have successfully answered questions from a prior paper does not guarantee that they'll want to publish your paper; I've had it happen both ways) and most of the journals that I've submitted to have been for less logical reasons than this (the other common strategy, related to yours, is to look through your bibliography and see whether any journal comes up more than once; if it does, if your paper is similar in subject matter and scope to any of those journals, then it's at least reasonable to submit there).
Here's an idea: why don't you come up with one or two more ideas for where to submit your paper which feel different from Linear Algebra and its Applications: e.g. try a journal which does not specialize in a mathematical subfield; try a journal which is of significantly higher quality -- e.g. Discrete Mathematics; if it doesn't sound ridiculous, maybe try something like the American Mathematical Monthly. Then bring these specific journal suggestions back to your advisor and ask for feedback. If you don't get any feedback from this, that's strange, and it is probably worth asking (as sunnily as you can possibly muster) why you're not getting help on this.