I have been wondering about this for a long time, and I can't seem to reach a solid conclusion. If temperature of an object is related to the movement of its atoms, then is it true to say that a moving object have a higher temperature?
I am currently in grade 12. I really like neuroscience and physics (more towards physics) and would like to pursue them in university. Would it be a good idea to do a physics and neuroscience double major or something? I'm thinking of really trying to combine the two, so that I do physics...
I believe I understand it! Could you please check if I've got it right?
Assume y ∈ im A
then y = Ax = (AVV-1)x
y = AV(V-1x)
since V-1x ∈ Rn, then y ∈ im(AV) and im(A) ⊆ im(AV)
Assume y ∈ im AV
then y = AVx = A(Vx)
since Vx ∈ Rn, then y ∈ im(A) and im(AV) ⊆ im(A)
Therefore im(A) = im(AV).
If A is an mxn matrix, show that for each invertible nxn matrix V, im(A) = im(AV)
The Attempt at a Solution
I know that im(A) can also be written as the span of columns of A.
I also know that AV = [Av1 Av2 ... Avn]
so im(AV) is the span of...
That's not what I originally meant. What you're saying is that the speed of the satellite is too low to stay at orbit at R, and because of that a rocket pointing away from Earth exerts an outward radial force on the satellite to keep it in orbit.
What I meant is the exact opposite. The...
Sorry I may have used the wrong wording. What I meant is that the satellite cannot orbit the earth in a circular trajectory with that V and R, and because of that a rocket it helping it stay in an orbit by exerting a force directed towards the centre of the Earth. So the satellite is not...
Assume that a satellite(mass m) is orbiting the Earth(mass M) at radius R and speed V (the orbit is circular). The satellite is in a position such that the force of gravity exerted on it by the planet is not enough to keep it in orbit. Therefore, the satellite has an engine, which always points...
Thanks a lot! Is this method the same as the methods mentioned by the other members? I fail to see a similarity. If this is a different method, how many ways of finding an the basis of an image are there in total?