Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". If an nxp matrix U has orthonormal columns, then UUTX= x for all x in R". Let W be the subspace spanned by the columns of U. Then UTUX = projwyx. If p = n, then W for all x in R". If p

Elementary Linear Algebra (MindTap Course List)
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Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R".
If an nxp matrix U has orthonormal columns, then UU'x=x for all x in R".
Let W be the subspace spanned by the columns of U. Then UTUX= projwx. If p=n, then W
be all of R", so the statement is
The statement is
be all of R", so the statement is
for all x in R". If p<n, then W
for all x in R".
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". If an nxp matrix U has orthonormal columns, then UU'x=x for all x in R". Let W be the subspace spanned by the columns of U. Then UTUX= projwx. If p=n, then W be all of R", so the statement is The statement is be all of R", so the statement is for all x in R". If p<n, then W for all x in R".
The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the
vectors are in the order x, and x2.
6.
- 2
The orthogonal basis produced using the Gram-Schmidt process for W is
(Use a comma to separate vectors as needed.)
Transcribed Image Text:The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order x, and x2. 6. - 2 The orthogonal basis produced using the Gram-Schmidt process for W is (Use a comma to separate vectors as needed.)
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