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Introduction to Linear Algebra Quiz #8
1. (a)
is an
×
matrix and
is a vector in
. What is a least squares solution
of
?
A least squares solution of
is a vector
in
such that
∥
∥
≤
∥
∥
for
all
in
(b) Every subspace of
has an orthonormal basis. Is this statement true?
No, the zero space has no basis.
2. Let
be an
×
matrix with linearly independent row vectors. Find the standard
matrix for the orthogonal projection of
onto the row space of
.
The row space of
is
. Thus the orthogonal projection of
onto
is the identity
transformation. The standard matrix is the identity matrix
.
3. Use the GramSchmit process to transform the given basis into an orthonormal basis.
{
} where
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This note was uploaded on 05/19/2008 for the course MS 4032 taught by Professor Anony during the Spring '08 term at A.T. Still University.
 Spring '08
 anony

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