Recent content by Easy_as_Pi

Hey sorry I haven't replied yet; I had work from 8am-7pm today. Bacle2, they are linearly independent, but I'm not quite sure what you mean by extending the subspace. That might not be something my class has covered yet (our book seems to go in a different order compared to note sets I have...

If I let A be the matrix whose rows are given by the three vectors that span W, then find the null space of that matrix, the result would be all vectors x, such that Ax=0. Yet, this is just the null space of the subspace I've been given, not a null space of matrix such that the null space is the...

Homework Statement Give a matrix B so that the subspace W defined in part b (W = (1,1,0,-2),(1,-1,1,6),(0,1,1,4)) can be written as W = N(B) where N(B) is the null space of B Homework Equations none that I know of, other than N(A) = {vectors x | Ax = 0} The Attempt at a Solution...

I'm not quite sure I follow. I ended up answering it this way: Eddy's definition implies there is a single natural number, N, such that for all n>N |1/n|< every epsilon greater than zero. Which is not true. For every epsilon you give me, I can find an N such that 1/n is less than that epsilon...

Homework Statement Eddy wrote on his midterm exam that the definition of the limit is the following: The sequence {an} converges to the real number L if there exists an N ∈ Natural numbers so that for every \epsilon > 0 we have |an − L| < \epsilon for all n > N. Show Eddy why he is wrong by...

Sorry that I took an eternity to reply. I was at a study session for linear algebra. Thanks so much, Dick. I think you've helped on every question I've posted here. I really appreciate it. I tripped myself up by only thinking about positive sequences. I took increasing and mistakenly correlated...

Homework Statement Give an example to show that it is not necessarily true that the product of two eventually increasing sequences is eventually increasing. Homework Equations a sequence is eventually increasing if for N\in natural numbers, a_{n+1} \geqa_{n} for all n>N. The Attempt...

So, to make sure I'm following you, Mark44, I would end up with a function r of s and t. OP= <1,1,-1,2>, u=PQ=<1,2,1,-1> , and v=PR=<0,1,3,1>. r(s, t) = OP + su + tv r(s, t) = <1,1,-1,2> + s<1,2,1,-1> + t<0,1,3,1> I know I need to have a point in the plane and two vectors from that point...

Homework Statement Find a parametric equation of each of the following planes: d) The plane in R4 containing the points P: (1,1,-1,2), Q: (2,3,0,1), and R: (1,2,2,3) The Attempt at a Solution I found vector PQ <1,2,1,-1> and vector PR <0,1,3,1> My next thought was to find a vector...

Oh wow, I can't believe I missed that! Thanks for that!

Homework Statement Let A = {1,2,3,4}. Give an example of a relation on A that is symmetric and transitive, but not reflexive. Homework Equations Symmetric: if aRb then bRa Transitive: if aRb and bRc then aRc Reflexive: aRa for all a in A The Attempt at a Solution {(1,2),(2,1),(1,1)}...

Homework Statement The count in a bacteria culture was 900 after 15 minutes and 1400 after 30 minutes. What was the initial size of the culture? What is the doubling period? What is the size after 70 minutes? When will the population reach 11000? Homework Equations P0= 900/e15k=1400/e30k...

Micro, you have came to rescue on a few of these problems for me. I really appreciate it. I don't think I have to fill it out in the way I did, but I was following the example in my book. None of them had three variables. Your method seems like the best. Thanks!

Homework Statement For statements P, Q, and R, use a truth table to show that each of the following pairs of statements are logically equivalent. a) (P^Q) <=> P and P=>Q b) P=>(Q v R) and (~Q)=>(~P v R) The Attempt at a Solution See attached truth tables. Basically, I have no idea how to...

Awesome. All clear now. Mark this one solved. Thanks for all the help!