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:

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- Dec 11th 2007, 01:55 PMakhayoonorthogonal 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: - Dec 11th 2007, 04:34 PMkalagota
- Dec 11th 2007, 05:04 PMakhayoon
well, thanks but...what about the rest?:)

- Dec 12th 2007, 03:06 AMbadgerigarQuote:

Y = [2 1 -1 1] - [1 -2 1 -1]

Writing Y with respect to this basis is (-1,1)

so (-1,1)$\displaystyle \bullet$ Z = 0

so Z can be span{(1,1)}

so Z can be span {(3,-1,0,0)} - Dec 12th 2007, 03:26 AMakhayoon
:confused::confused:

so you're proving that Z is orthogonal using the dot product? - Dec 12th 2007, 03:29 AMbadgerigar
I think you need to revise the definition of orthogonal.