Null space Definition and 71 Threads

Homework Statement Ax=b where, A = 2 -1 ...-1 2 Homework Equations a) Find Null Space N(A) and Column Space C(A) b) For which vectors b does the system Kx=b have a solution? c) How many solution x does the system have for any given b? The Attempt at a Solution a) For Null Space, I...

Homework Statement Given a linear operator T, show that if rank(T^2)=rank(T), then the range and null space are disjoint. So I know that I can form a the same basis for range(T^2) and range(T), but I'm not sure where to go from there.

There are 2 issues I want to talk about in this post. (1) General algorithm for gauss-jordan elimination computation of null space (2) Closed form solution to 3x3 null space Following the example here, https://en.wikipedia.org/wiki/Kernel_(linear_algebra) I thought a general algorithm to...

Homework Statement Let (u,v,w) be a basis for vector space V, and let L be a linear transformation from V to vector space W. If (L(u),L(v),L(w)) is linearly dependent, then dim(Null Space(L)) > 1. Homework Equations The Attempt at a Solution I don't see why dim(Null...

Homework Statement find a basis of the null space N(A) in R^5 of the matrix A = 1 -2 2 3 -1 -3 6 -1 1 -7 2 -4 5 8 -4 in M3*5 (R) and hence determine the dimension Homework Equations The Attempt at a Solution i found that A= 1 -2 2 3 1 0 0 1/5 2/5 -2/5 0 0 0 0 0 by...

I am just wondering what is meant when someone says the Col A is a subspace of null Space of A. What can you infer from that? Also what is a null space of A(transpose)A How do they relate to A? Are there theorems about this that I can look up?

got a question show that the null space of T is a vector space of U given the mapping T:U->V i know that null space or kernal of T is kerT={uEU: T(u)=0} and is a subset of U but don't have a clue where to start applying this to my question?

Homework Statement What are the basis for the row space and null space for the following matrix? Find the dimension of RS, dim of NS. [1 -2 4 1] [3 1 -3 -1] [5 -3 5 1] Homework Equations dim RS + dim NS = # of columns The Attempt at a Solution I reduced the matrix into...

Homework Statement Find null space of A, NS(A) and sketch NS(A) in R2 or R3. A = [1 3 2; 2 6 4] Homework Equations AX = 0 The Attempt at a Solution I know the second row is twice the first one. I tried to solve for x1, x2 and x3 putting everything in the form of AX =0. I did...

If V is any vector space and S and T are linear operators on V such that ST=TS show that the null space and the range of T are invariant under S. I think I need to begin by taking an element of the range of T and having S act on it and show that it stays in V? Can you help get me started?

[SOLVED] basis of a null space Homework Statement Find a basis of the null space N(A)\subsetR^5 of the matrix A= 1 -2 2 3 -1 -3 6 -1 1 -7 2 -4 5 8 -4 \inM3x5(R) and hence determine its dimension Homework Equations The Attempt at a Solution...

Find the Dimension of the null space of the given matrix A: | 1 3| |-2 -6| The Attempt at a Solution I honestly don't know how to work this at all. I think I'm confused as to what Null Space actually is, so that's making this a difficult problem to understand. please help.

I need to find the null space of: \dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right) so: \dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right) \binom{x}{y} = 0...

Homework Statement I am trying to find the matrix M that projects a vector b into the left nullspace of A, aka the nullspace of A transpose. Homework Equations A = matrix A ^ T = A transpose A ^ -1 = inverse of A e = b - A x (hat) e = b-p I know that the matrix P that projects...

Hihi I've been working on this problem for some time: if A is a (m x n) matrix, and A' denotes its transpose, then the null space of A is equal to the null space of A'A. Is this always true? I thought of a proof for the special case where A is given in reduced row echelon form, but fail to...

could someone kinda explain in plain english what null space is? @@

Let V denote the vectore space of continuously differentiable functions, ƒ, over the interval [0,1] such that ƒ(0)=0. Suppose Φ is-contained C∞ [0,1] (set of infinitely differentiable functions over the interval [0,1]) and define the operator TΦ:V→R:ƒ→∫ƒ'(x)Φ(x)dx 0,1 Describe the null space...

Hello everyone I'm confused on finding the null space on this problem: the matrix is: 0 2 0 -5 0 1 4 0 0 0 1 0 0 0 0 1 null(A) = 2b - 5d = 0 b + 4c = 0; c = 0 d = 0; b = 0; a = ? You don't know what a is, so I'm quite confused. Any help?

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...

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...

How can I determine the null space for the 2 x 6 zero matrix as precisely as I can? Clearly N(A) = {x: Ax = 0, x in R^n}, So if A is this 2x6 matrix, wouldn't virtually any vector x that is in R^6 work? This is supposed to be a "conceptual" problem, and I KNOW it can't be this easy for...