# orthogonal basis

• December 11th 2007, 02:55 PM
akhayoon
orthogonal basis
U=span{[1 -2 1 -1], [ 2 1 -1 1]}. show that Y=[1 3 -2 2] is in U, and find all Z such that [Y,Z] is an orthogonal basis of U.

:confused::confused::confused:
• December 11th 2007, 05:34 PM
kalagota
Quote:

Originally Posted by akhayoon
U=span{[1 -2 1 -1], [ 2 1 -1 1]}. show that Y=[1 3 -2 2] is in U, and find all Z such that [Y,Z] is an orthogonal basis of U.

:confused::confused::confused:

Y = [2 1 -1 1] - [1 -2 1 -1]
• December 11th 2007, 06:04 PM
akhayoon
well, thanks but...what about the rest?:)
• December 12th 2007, 04:06 AM
Quote:

Y = [2 1 -1 1] - [1 -2 1 -1]
Notice that {[1 -2 1 -1], [ 2 1 -1 1]} is an orthogonal basis for U.
Writing Y with respect to this basis is (-1,1)
so (-1,1) $\bullet$ Z = 0
so Z can be span{(1,1)}
so Z can be span {(3,-1,0,0)}
• December 12th 2007, 04:26 AM
akhayoon
:confused::confused:

so you're proving that Z is orthogonal using the dot product?
• December 12th 2007, 04:29 AM