I barely see what it's asking...
Given A, I don't have a problem proving that A is a subspace of M22 -- just show there's closure under addition and multiplication. I can find a basis/span, etc.
For this question, I'm somewhat lost. Since A + B = M22, then B = M22 - A, I'm assuming B has...
This should make it easier haha
[PLAIN]http://dl.dropbox.com/u/907375/asd.jpg
In case the image isn't showing either, the symbol that isn't showing is the "R" for real numbers, so s,t in R and M(R)
Homework Statement
Let A be the following 2x2 matrix:
s 2s
0 t
Find a subspace B of M2x2 where M2x2 = A (+) B
Homework Equations
A ∩ B = {0}
if u and v are in M2x2, then u + v is in M2x2
if u is in M2x2, then cu is in M2x2
The Attempt at a Solution
Let B be the...
Homework Statement
Given the following 2-dimensional plane in R^4 written in parametric form:
x_1 = 1 + (-1)s
x_2 = 0 + ( 1)s
x_3 = 1 + (-1)t
x_4 = 0 + ( 1)t
a) find a 2-dimensional plane that does not intersect it
b) find a 2-dimensional plane that intersects it to form a point
c) find a...
Yeah, because I was shifting over the pair of ones by two every time, and hence decreased by n/2 total normals -- makes sense. I'm not quite sure why I did that; probably just didn't think about the easy math clearly enough.
So, just shifting the pair of twos will result in a different...
N3 = (0,0,1,1,0,0,...,0)
N4 = (0,0,0,0,1,1,...,0)
Yeah?
Because these would result in the following dot products (with AB):
(0+0+1-1+0+0+...+0)=0, thus normal
(0+0+0+0+1-1+0+0+...+0)=0, thus normal
I'm still having some trouble picturing this...
So for part (3), I need to find a plane that's normal to vector AB.
Let n be my normal vector, AB. I now have to calculate n.p, where p is some point that lies in the plane. I'll use A for my point since it wants it at the origin and A is all...
Homework Statement
In Rn, define A = (0, 0, ..., 0) and B = (1, -1, ..., (-1)n-1)
Find (1) the parametric form of the line through A and B, (2) as an intersection of (n-1) hyperplanes, and (3) the hyperplane crossing the origin, normal to AB.
Homework Equations
AB =...