Question

what is null-space in vector space?

Answer 1

In linear algebra, the kernel or null space (also nullspace) of a matrix A is the set of all vectors x for which Ax = 0.

Answer 2

The null space of an m × n matrix is a subspace of Rn. That is, the set Null(A) has the following three properties:
Null(A) always contains the zero vector.
If x ∈ Null(A) and y ∈ Null(A), then x + y ∈ Null(A).
If x ∈ Null(A) and c is a scalar, then c x ∈ Null(A).

Answer 3

http://en.wikipedia.org/wiki/Kernel_(matrix) for further details

Answer 4

nullspace is only for nx1 matrices?

Answer 5

no it is not necessary

Answer 6

null space is for mXn but the answer comes out to be nX1 matriz

Answer 7

In general, if you have two vector spaces V and W, and a homomorphism between them T
\[ T : V \to W \]
then the null space of T are the vectors in V such that T(v) = 0.

Notice the null space is a property of the homomorphism, not an intrinsic property of V.

Answer 8

is null space contain all the solutions of homogeneous system?

Answer 9

what is homomorphism?

Answer 10

yes all sol of homogeneous system will be in null space

Answer 11

whether the solution is trivial or non_trivial?

Answer 12

Does null space contain all the solutions of homogeneous system? Yes
what is homomorphism? A function between vector spaces the preserves important vector space properties. You can think of it for now as a matrix

Answer 13

yes trivial and non trivial both

Answer 14

ok now clear another concept please in null space we take matrices of any order but the ans should be nx1 matrix. right?

Answer 15

yes right

Answer 16

and augmented matrices should be homogeneous. we can't take non homogeneous augmented matrix. isn't it?