A question of 5 parts

1. Feb 5, 2008

transgalactic

i have solved a full question
(except the last part which i tried to come up with some formula but that didnt work out)

i showed every step of the way

unfortunetly i dont have the answers to this question
so can you tell me if i solved wrong some subquestion
and how to solve the 5th
it a realy challenge for me

1st page :

http://img260.imageshack.us/my.php?image=img8259zs8.jpg

2nd page:

http://img155.imageshack.us/my.php?image=img8261ge2.jpg

3rd page:

http://img401.imageshack.us/my.php?image=img8262iu8.jpg

2. Feb 5, 2008

HallsofIvy

Staff Emeritus
This looks good.

Since V has dimension 1, and the intersection with U is a subspace of V, the intersection must be either the trivial subspace (consisting only of the 0 vector) or V itself.

In problem 4, You have an orthogonal basis which is what they ask for. If they had asked for an orthonormal basis, you would need to divide each vector by its length.

For problem 5, you are told that, for linear transformation, A, A2+ A= -I and are asked to find A-1 (so you may assume that A has an inverse).
You have factored A2+ A= A(A+ I)= -I. I recommend you multiply both sides of that equation by A-1 and then solve for A-1.

An equivalent way to do the same problem is to write the original equation as I= -A2- A and multiply both sides of that equation by A-1.

3. Feb 6, 2008

transgalactic

so regarding the second page

you say that if the the solution is one vector
it always must be (0,0,0)