Recent content by Computnik

I feel like such an idiot now, that was my initial thought but I dismissed it because it felt like it was too easy to be the right answer. :redface:

I know that the ##(?)## ##(??)## are the normal to the line ##\langle x,y\rangle = \langle a, b\rangle + k\langle d_1,d_2\rangle##. However what I don't know is how you should obtain the normal for that line...

I'm a bit lost. :/ Any more tips?

I'm not sure what you mean with "eliminate the ##k## parameter". But I guess this is a start? ##x=a+kd_1## and ##y=b+kd_2## now let me put ##x## and ##y## into the "form" of the point-normal equation. Which I will call: ##p(x-x_0)+q(y-y_0)=0##, where ##p## and ##q## are constants. We...

Two questions: 1. (Perhaps a dumb question) Is ##\langle x,y\rangle## another way of writing a 2×1 matrix where x=a11 and y=a21? (I'm really new to linear algebra...) 2. If I'm correct about question 1, then I still don't see how I can "translate" ##\langle x,y\rangle = \langle a, b\rangle +...

Homework Statement Say that I have a problem along the lines of: Find the point-normal equation for the line L. L=u1+k*u2, where k is ℝ. And then I'm given u1 and u2, which both are 2×1 vectors. Then L will also be a 2×1 vector (which consists of a11 and a21), which I guess is ok (since it...

Homework Statement Hi, I have a really short (and dumb) question. In one of my homework problems they talk about a vector w, such that w=e1+e2+e3. (In R3.) The Attempt at a Solution I guess they mean that: e1=(1,0,0), e2=(0,1,0) and e3=(0,0,1). So w=(1,1,1). Right?

I was able to find the solution now. Thanks for all the help!

Yes you were right in assuming that I meant that! Follow-Up question: Which elements does O(n) contain and is there a way of knowing which elements (of O(n)) that satisfies det(x)=1 and which elements that satisfies det(y)=-1? I guess the first step would be to determine if the function det...

Follow-Up Question: Is it true that in order to determine whether or not det-1({1})⊂O(n) and det-1({1})⊂O(n) are groups I will have to show that they "hold" for the following? Let's say that det-1({1})⊂O(n)=G. i) The following is true x ° (y ° z) = (x ° y) ° z for all x, y, z ∈ G...

O(n) is the orthogonal group. Ok, I wasn't aware of that. Thanks!

Homework Statement This problem has two parts: i) Determine the range of det: O(n) → ℝ. ii) Are det-1({1})⊂O(n) and det-1({1})⊂O(n) groups? Homework Equations AA-1=I & AAT=I The Attempt at a Solution i) det(AAT)=det(I) det(AAT)=1 det(A) det(AT)=1 det(A) det(A)=1...