Recent content by leden

By full-rank, I mean rank(M) = min{num_cols(M), num_rows(M)}.

Say I have a mxn matrix A and a nxk matrix B. How do you prove that the matrix C = AB is full-rank, as well?

Suppose you are building a sequence consisting of 0 and 1 in such a way that: - you start with 1 - no consecutive 0s are allowed Examples of such sequences are: 1, 1010, 110111101 etc. Empty sequence is also allowed. I want to prove by induction that the number of 0s in such a sequence is...

Thanks, let me try to solve now... \frac{ds}{1+{s}^2}=dt \int\frac{ds}{1+{s}^2}=\int dt \arctan s=t s(t)=\tan t Now v(t)=\frac{ds}{dt}=\frac{\tan t}{dt}=\frac{1}{{\cos}^{2}t} This is strange, because it seems that velocity is practically infinity at point t = pi/2.

I am aware of that.. But the problem is that am not so much familiar with calculus and when it comes to physics I don't know what to do when integrating/differentiating some functions which is dependent on many variables... The first things that bothers me is whether it is correct that...

I have spent a long time stuggling with an interesting problem which was set up by my brother some time ago: Consider an object that starts moving along the line according to the equation below: v(s)=1+{s}^{2} where s is the total distance traveled by the object and v is the velocity of the...

I wonder how could I calculate impact force of an object (eg. a stone) in a free fall impacting on the perfectly inelastic (perfectly hard) floor. I know: - m -mass of the falling object - h -height of the fall - v -speed at the time of impact - t -time it...