Question

0

Answer 1

Any eigen value(\(\lambda \)) satisfies below equation, yes ? \[\large \rm Ax = \lambda x\]

Answer 2

plugin \(\lambda = 0\)
\[\large \rm Ax = 0x\]
\[\large \rm Ax = 0\]

doesn't that mean there exists a nonzero vector \(\large \rm x\) that solves the above eqn ?

Answer 3

Can I give you 2 medals @ganeshie8

Answer 4

In light of above observation what can you conclude about the nullsapce of A ?

Answer 5

Kai xD

Answer 6

yes kai you can with a little help you can

Answer 7

@ganeshie8 i can conclude that there is no nullspace?

Answer 8

nope, nullspace of a matrix always contains the zero vector. so ts never "no nullspace"

whats the definition of nullspace/nullity according ur textbook ?

Answer 9

lemme check

Answer 10

The nullspace of A consists of all solutions to Ax = 0

Answer 11

The nullity is the dimension of the nullspace. As ganeshie8 demonstrated, there is certainly one non-zero vector, the eigenvector corresponding to eigenvalue 0, that is sent to 0. Therefore the dimension of the nullspace is at least 1.

Answer 12

@ganeshie8 said that nonzero vector solves for Ax =0. How do we know that its nonzero?

Answer 13

An eigenvector by definition is non-zero.

Answer 14

Ahhh! Got it! SO there is atleast one no matter what! thanks