Prof. A. Suciu
MTH 1230 -- Linear Algebra -- Fall 1997
Sample Quiz 4
Find the least squares solution of the inconsistent system
for
Find the equation of the least-squares line that fits the following data points:
Sketch the resulting line. What is the predicted value of
y
at
x
=6, based on this model?
Let
Find an orthonormal basis for the subspace of
which has
as a basis.
Use part one to find the
QR
factorization of the matrix
.
Let
Find the eigenvalues of
A
.
Find a basis for each eigenspace of
A
.
Find a diagonal matrix
and an invertible matrix
S
such that
.
[You do not have to calculate
S
-1
.]
A
matrix
A
has first row
and eigenvalues
and
.
Find
A
.
What are the eigenvalues of
A
-1
?
Compute
, where
I
is the identity
matrix. Explain your result.
A
matrix has eigenvalues
.
Find the eigenvalues of
A
2
.
Find the trace of
A
2
.
Find the determinant of
A
2
.
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Created by Alexandru Suciu, Tue Nov 18, 1997
alexsuciu@neu.edu
http://www.math.neu.edu/~suciu/mth1230/1230f97.sq4/index.html