Question

Vector subspace question!!
http://i.imgur.com/CXznr5g.png

I thought d & e would be false but the rest would be true... D doesnt hold because if det(a)=0 then the 4th axiom ( the o one) would not hold, If I understand this right?

Plus e would not hold because if it is all integers then K could be a fraction, not fitting in the restriction. no>?

Answer 1

why do you think F holds ?

Answer 2

scalar multiplication will not change symmetry
does adding/subtracting two symmetric matrices produce another symmetric matrix ?

Answer 3

hum, I was thinking because if it is symmetric it would be a transpose no? and A^t=A

Answer 4

because A^t = A then I can say A+B= B + A ( axiom 2) so A^t+B^t = A + B

Answer 5

Ahh yes you're right, adding/subtracting two symmetric matrices should result in a symmetric matrix

Answer 6

everything forms a subspace except for d and e

Answer 7

that is what I put and I still get it wrong which troubles me :/

Answer 8

looks you forgot to check the last option

Answer 9

A C and F are the answer... how isn't b part of it O.O

Answer 10

if b is with a 0 above and under the diagonal, it should always stay the same no? I mean multiplying a scalar won't change the 0s neither will adding the 0 matrix ( which in this case would be all 0s... unless that isn't considered row echelon form?)