Are you smart enough to know?

Question

What comes next?

1
11
21
1211
111221
312211
13112221
1112213211
?

Answer 1

yes i am
312211131221 - comes next

Answer 2

Hello
unique solution equivalent to kernel 0
I am having hard time understanding the statement above. tried to
think about it with examples, google and all.
from what I understand, the kernel is a subspace of the domain. so
given T: R^n -> R^m, kernel {0} is a vector in R^n with all its
elements equal zeros.
let x be a vector in R^n, i.e. a vector of the unknowns, the linear
transformation T(x) = b, T has at most one solution for every b if and
only if Ker T = {0}, this last statement is whats confusing me allot.
here is what it means to me:
T has at most one solution implies the values of the unknowns in the input
vector x
Ker T = {0} implies the values of the unknowns in the input vector x are
all zeros.
if what I understand is correct, then why don't we just say that all
unique solutions, i.e. all unknowns are zeros. if we do, then how can
the following system of linear equations have a unique solution which
is not a zero vector,
x - 3y = 0
x - y = 3
clearly it has a unique solution and it is not equivalent to kernel 0
thanks

Answer 3

Lets see

41321143111

Answer 4

easy peasy. 312211131221.

Answer 5

uuuhhhh


[brain blast]

Answer 6

4122...21