Construct a 2x2 matrix that is not the zero vector

[Karma]

Construct a 2x2 matrix that is not the zero vector yet satisfies A^2=0 been studying this question for a while...any help?

 

[yenchin]

Do you mean A is a 2x2 matrix which is not a zero matrix, and it is such that A^2 = 0 ?

 

[matt grime]

a) think geometrically

OR

b) think in terms of basis vectors

OR

c) just do it - write out a general a,b,c,d matrix square it and see what choices of a,b,c,d would mean its square is 0.

 

[FunkyDwarf]

Look up nilpotence too, won't help you solve the question but its interesting and related to it :)

 

[HallsofIvy]

Or even, just write out a matrix

[a b]
[c d], square it and see what equations must be satisfied to be the 0 vector!