Recent content by kamui8899

Hi, I was working on a problem and I can't figure out what I'm supposed to do. It reads, find the vector in subspace S that is closest to v; write v as the sum of a vector in S and a vector in S^a; and find the distance from v to S. S spanned by {(1,3,4)} v = (2,-5,1) Ok, what I did was...

Thanks for the reply. You may have to help me out here a bit, as far as I know the notation means that t is an element of all real numbers such that it is equal to the equation for some natural number n. Thus every natural number has some t value, so we have to find the inverse of the...

Hello, I was having trouble proving that two functions are one to one and onto. For one: S = {x is an element of all reals: x = (n^2 + sqrt(2))/n, n is an element of naturals numbers} Define f: Natural Numbers -> S by f(n) = (n^2 + sqrt(2))/n We have to show that f is onto. So I...

I have an augmented matrix: 1 2 3 4 0 3 4 5 3 12 1 2 Now this matrix simplifies to: 1 2 3 4 0 3 4 5 0 0 0 0 So there are infinite solutions, however I have to write all the solutions to the equation. I wanted to do this with vectors. So I first solved for x and for y and got...

Basically I figured out the answer to question 1, however my main problem is finding out how to write the basis for problem 2 as vectors. That, and I'm still working on problems 3 and 4, any help is greatly appreciated!

I posted before about Null Spaces and, after some review, I think I have a grasp on it. However I have a few more general questions, so I thought I'd start a new thread (although there may be some redundancy) Problem 1: Find the dimension and a basis for the Row, Column, and Null Spaces...

Thanks for the reply. So what your saying is if I had to give the number of dimensions of the subspace defined by 7x -3y 1z = 0, that the dimension would be 2, with one dependent variable (z), and that the basis of this subspace is: -7 3 1 0 0 1 ?

I have another question, its related to what we did earlier: Question: For the linear map of L, find the dimension of and a basis for the null space of L and the Image of L. L: P ^ 2 -> R^1 where L(P) = the integral from 1 to 3 of (p(x) + derivative(p(x+1)) dx) I started with a basis of...

The question is: For each of the following subspaces, find the dimension and a basis: {(x,y,z) are elements of R^3: 7x - 3y + z = 0} I had actually posted about this before, but I'm confused as to what the Null space is here. So, z = -7x + 3y, so there is one dependent variable and two...

Thanks for the reply, that's what I did, or at least meant to say before. It seems I posted a solution to a different problem. So far you've been an immense help, as most of this makes sense now, however I have a few last questions I'd like to ask. Find the dimension and basis of the...

Thanks a bunch! It makes a lot of sense once I see it, it just takes me awhile to figure it out. I have another question. {p(x) is an element of P^3: p(3) = p(4)} Find the dimension and a basis So p(x) = a + bx + cx^2 + dx^3 Where p(5) - p(-3) = p prime (2) So I just have to plug...

I think I understand how to do this, but I wanted to double check my work. I have to find the basis of the null space for the matrix: 1 0 2 0 0 7 So I knew that the basis of the image had two dimensions and a null space of one. The first and third columns are linearly independent (or at...

I was in the middle of proving something when I reached a contradiction, that .5 + an integer = an integer. However, this cannot be true, and I'm curious if its acceptable to just say that by definition of integers .5 + an integer is not an integer, or do I have to prove it? Furthermore, if...

Can you specify the direction of the torque you indicated occurred in the second part of your explanation, I'm assuming you mean that the person holding the rock will fall off the cliff due to this torque. Essentially then, there is no way to prevent the person holding the rock from falling by...

I came across a particular result which bothered me, it stated that: Result: A person bending to 90 degrees at the waist with their back to a cliff will fall because their center of mass is past their feet. This statement perturbed me, because, when I applied it myself, I found that, while I...