Recent content by boaz

a simple trick that helped me out is taking a paper and like the computer going over each line and writing what is stored in the variables. it sounds odd and like a waste of time, but for a newbie is a life-saver.

what about stop_pow = 4096 base = 2 # print the seq. 2, 4, 8, ..., 4096 while (base <= stop_pow): print base base = base*2 does it work?

i think you almost nailed it. i would separate it to 2 sections. one - no repeating. in this particular case, we choose 8 letters from 26 and count all the ways we can order them, which is what you've mentioned \frac{26!}{(26-8)!} two - one letter repeats. in this one, we choose only 7 letters...

the second line from the end looks incorrect. \frac{1}{k\cdot r^2} \le 0 \Leftrightarrow k<0, r\ne 0 why won't you try to attack it from another aspect. for example, p_1>p2>0 \rightarrow \frac{1}{p_2}>\frac{1}{p_1}

it seems like you know the answer but don't know how to do this. so first of all, let's state that "in order to prove that the space of 2×2 real matrices forms a vector space of dimension 4 over R. we will define an isomorphism from 2x2 real matrices space to R4". Later, we will say. "lets take...

I guess I wasn't much clear. What I meant is that T takes a matrix [a,b;c,d] and gives a vector (a,b,c,d). Actually, I think that this is what he has meant.

If I understood right, we have to find an isomorphism from M^{R}_{2x2} to R^4. In other word, we need to find a linear transformation, T:M^{R}_{2x2} \rightarrow R^4 that ker(T)=0. HINT: look at T[a,b;c,d]=(a,b,c,d)

4x^2=7y \rightarrow 4x^2+0x+0=7y \rightarrow (4/7)x^2+0x+0=y thus, the focus is (-\frac{0}{2\cdot(\frac{4}{7})}, -\frac{0^2}{4\cdot(\frac{4}{7})}+0+\frac{1}{4\frac{4}{7}} ) = ( 0, \frac{7}{16} ) the same thing goes with the directrix. hope it helped.

It seems fine to me, except the last one. In general, you get the total number of combinations and divide it by the number of winning combinations in each ticket, as a result you get the number of tickets. For instance, in the 2nd question, we have C(6,2) combinations. However, each ticket has...

I am not sure, but when saying T=[1,3; 2,6] is relative to E, it means that T*e1^t=(1,2) T*e2^t=(3,6) Am I correct? If I have remembered correctly, then we want to find T' such that T'*(1,2)^t=(1,2) T'*(-3,1)^t=(3,6) or in other words [a,b;c,d]*(1,2)^t=(1,2) => (a+2b,c+2d)=(1,2)...

The location is great. The problem is how one, who doesn't own a car, can get there. By the way, when does it start?

Hehehe, good guess. What are the odds? I see you have gotten some reputation here. :-)

Sounds good, just what are the prerequisites? Judging by the cover of the book, it seems more than just Analysis. Anyway, more details regarding the online study group are welcome.

Moreover, notice that Sp(B1)+Sp(B2)=Sp(B1uB2), where B1,B2 are sets or bases (in our case).

In general, if at least one of them is singular then AB is singular, and that's good enough to prove it. Another way to prove this is using determinant. Since |A|=0 and |B|=0 (A and B are singular), we get |AB|=|A||B|=0 => AB is singular too.