Recent content by johndoe3344

I came across this: Show that if p denotes an odd prime, then 2^((p-1)/2) = +1 (mod p). So basically, this is asking me to show that p|2^((p-1)/2)-1 AND p|2^((p-1)/2)+1 But I'm stuck from there. What am I missing? Could someone help me with the proof?

I was reading about this topic of my own leisure, and I came across something that I couldn't quite understand. The solution of Galileo's Paradox is that the set of natural numbers and the set of perfect squares are both infinite sets of the same cardinality (namely aleph 0). This I can...

Hi, thanks for your response. What do you mean my shorthand? I only said that B = A transpose because I didn't know how to write the superscript T on the forums (is that what you meant?) Does showing that ker(A^T*A) is a subset of ker(A) show that they are equal?

B= A transpose What is the relation between ker(BA) and ker(A)? I was told that they are equal to each other, but I can't figure out why. ker(A) => Ax = 0 ker(BA) => BAx = 0 so that BA is a subset of A. This shows that ker(BA) =0 whenever ker(A) = 0, but how does this also show that...

Homework Statement A library of randomly synthesized duplex DNA strands (length = 6 bp) is generated. What percentage of these sequences would you expect that the restriction enzyme BamH1 (restriction site = GGATCC) would recognize? a. 0% b. 0.02% c. 0.48% d. 0.07% Homework...

Thanks a lot. That cleared it up for me.

Homework Statement Not really a textbook question, but I've read from numerous sources that changing the concentration of the reactants/products won't change the equilibrium constant. Why isn't this contradictory? Assume the reaction: xX + yY <---> zZ where x,y,z are the coefficients of...

I found this in my notes, and I memorized it, but I have no idea why this is. Could anyone shed some light: Given: A mutation in A gives repressed reporter expression, while a mutation in B gives constitutive reporter expression. If: A double mutation in A and B gives repressed reporter...

I've been reading a bit, and I thought I understood it, but now I'm really confused: I know that hydrophobic forces at room temperature are almost entirely entropy driven: because a system aims for maximal entropy, it pushes non-polar molecules into an aggregate in order to reduce the...

So since multiplying each row of a scalar by the constant gives us det(B) = k*det(A)... If we multiply each row of a n x n matrix by the same constant, i.e. n times, then the formula would be for the case of k = -1: det(B) = [(-1)^n]*det(A) Which would explain the difference for odd n...

Why are we multiplying each individual row/column by a scalar? When we multiply the matrix by a scalar, doesn't this automatically distribute the scalar to every single entry of the matrix? I guess what I'm confused at is this: Suppose we let the square matrix B be obtained from matrix...

For an n x n matrix A, what is the relationship between det(A) and det(-A)? I tried it with a 1x1 matrix, and det (-A) = - det (A) I tried it with a 2x2 matrix, and det(A) = det(-A) I tried it with a 3x3 matrix, and the results were the same as that with a 1x1. This leads me to believe...

Thanks for all the help. But wait, so is the solution unique or not unique?

I follow up to this part: "where [v]_(u) is the coordinate vector of v in the base (u) which is a column vector." What do you mean specifically? What would be the basis of u? Is it [1,0,0] [0,1,0] [0,0,1]? If so, how would I go about constructing [v]_(u)?

Find an orthogonal transformation T from R3 to R3 such that T of the column vector [2/3 2/3 1/3] is equal to the column vector [0 0 1] So I tried to construct out the 3x3 matrix [a b c] [d e f] [g h i] and applied the properties of an orthogonal matrix and basic algebra. I ended up with a...