Let not all equal to zero and

Find a subspace Y such that and deduce X is 2 dimensional.

I am lost on this one.

Note:

is the external direct sum define as

If , then can be define as that is the internal direct sum

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- Sep 10th 2011, 10:31 AMdwsmithX circle plus Y = R^3
Let not all equal to zero and

Find a subspace Y such that and deduce X is 2 dimensional.

I am lost on this one.

Note:

is the external direct sum define as

If , then can be define as that is the internal direct sum - Sep 10th 2011, 11:07 AMHallsofIvyRe: X circle plus Y = R^3
It should be obvious that this is a plane and that the vector is perpendicular to the plane.

- Sep 10th 2011, 01:01 PMdwsmithRe: X circle plus Y = R^3
- Sep 10th 2011, 03:41 PMHallsofIvyRe: X circle plus Y = R^3
Y is the subspace spanned by . That is the space of all vectors of the form where can be any real number.