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
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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".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc357075-d330-4116-93bc-b2819b26405c%2Ffe333f0d-0431-4aa0-b120-000208709c43%2Fsdoknc_processed.png&w=3840&q=75)
![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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc357075-d330-4116-93bc-b2819b26405c%2Ffe333f0d-0431-4aa0-b120-000208709c43%2Fh6o4r1q_processed.png&w=3840&q=75)
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