Let
Find
an orthogonal matrix P and a diagonal matrix D
with A =
PDP
Use the permutation definition of the
determinant to find the determinant of
Find the inverse of A
if Calculators are permitted on this part
Consider the matrix
A.
Determine the rank of A. B.
Find a basis for the null space of A. C.
Find a basis for the column space of A using
columns of A.
A.
Prove
that B.
Let
Show that the set
is a basis for M
Graph the equation and write the equation in
standard form.
4x
One of the
following is a subspace of the space of differentiable functions.
I. {f | f(0) – f ‘(0)
= 1}
II. {f
| f(1) =
f ‘(1)}
A.
Determine which is not a subspace
and explain why. B.
Prove
that the other one is a subspace.
Prove that if A
is a matrix such that A
Answer the following true or false. If it is
true, explain why. If it is false
explain why or provide a counter example. A.
If v}
is a linearly independent set of vectors in R_{2}^{3}
and v_{3} is not in the span of S,
then {v,_{1}
v, _{2}v}
is a basis for R_{3}^{3}.
B.
Every orthonormal set of five vectors in R C.
Let A and B be
matrices such that A (A
+ B) |