find a matrix C such that AC=0?

Question

1 2 6
A= 0 5 4
0 0 3

Answer 1

if C is a matrix then 0 isn't a number
you need to tell me more about the elements of A???

but if i had to go on what you've just given me, C could be:
the zero matrix - that is a matrix with all elements equal to 0
in general suppose A is 2x2 matrix and C is a 2x2 matrix and that their product is equal to the 2x2 zero matrix and the elements of A in the first row are a11 and a12 and the elements in the second row are a21 and a22
the elements of C in the first row are c11 and c12 and the elements in the second row are c21 and c22 then given that yoiu know all the elements of A you need to find the elements of C such that a11*c11+a12*c21=0
and a11*c12+a12*c22=0
and a21*c11+a22*c21=0
and a21*c12+a22*c22=0

ok then.....................here we go
c11+2(c21)+c31=0
c12+2(c22)+6(c32)=0
c13+2(c23)+6(c33)=0
5(c21)+4(c31)=0
5(c22)+4(c32)=0
3(c31)=0
c31=0
3(c32)=0
c32=0
3(c33)=0
c33=0
5(c22)=0
c22=0
5(c21)=0
c21=0
c11=0
c12=0
c13=0

C is a zero matrix!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

It depends on the value of A.

Answer 3

could always make C a zero vector.