Let be the linear transformation defined by .

Q: Let . Find the coordinate vectors of relative to

Not sure how to put everything together, some guidance would be greatly appreciated.

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- October 22nd 2009, 11:46 PMLexyLeiacoordinate vector help
Let be the linear transformation defined by .

Q: Let . Find the coordinate vectors of relative to

Not sure how to put everything together, some guidance would be greatly appreciated. - October 23rd 2009, 05:08 AMHallsofIvy
The "coordinate vectors" of any vector u is the ordered triple (a, b, c) where a(1,0,1)+ b(1,1,0)+ c(0,1,1)= v.

So you need (a,b,c) such that a(1,0,1)+ b(1,1,0)= c(0,1,1)= (1, 0, 0).

That is the same as saying (a, 0, a)+ (b, b, 0)+ (0, c, c)= (a+b, b+ c, a+ c)= (1, 0, 0) or a+b= 1, b+ c= 0, a+ c= 0. Solve those equations for a, b, and c.

"T" has nothing to do with this question! - October 23rd 2009, 12:12 PMLexyLeia
- October 23rd 2009, 06:11 PMHallsofIvy
You

**said**"find the coordinate vector of , , and " and those are usual notation for the standard basis vectors of , (1, 0, 0), (0, 1, 0), and (0, 0, 1), respectively.