Construct a 2x2 matrix that is not the zero vector

1. Oct 12, 2007

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?

Last edited: Oct 12, 2007
2. Oct 12, 2007

yenchin

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

3. Oct 12, 2007

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.

4. Oct 19, 2007

FunkyDwarf

Look up nilpotence too, wont help you solve the question but its interesting and related to it :)

5. Oct 19, 2007

HallsofIvy

Staff Emeritus
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!