The vectors
u = and
v = span a plane in
R3. Find the projection matrix P onto
the plane, and find a nonzero vector b that is projected to zero.
BITMAPSETAnswer0.2214in0.205in0ina1
2.
For the following matrix, find the characteristic
polynomial, minimum polynomial, eigenvalues, and eigenvectors. Discuss the
relationships among these, and explain the multiplicity of the eigenvalue.
BITMAPSETAnswer0.2214in0.205in0ina2
3.
Which of the following statements are correct for the
matrix
A = ? The set of all solutions
x = of the equation
Ax = is the column space of A; the row space of A; a nullspace of A; a plane; a line; a point.BITMAPSETAnswer0.2214in0.205in0ina3
4.
The matrices that rotate the xy-plane are
Aθ = . Verify that
AθA = Aθ + and
A - θ = Aθ, using matrix products and trigonometric
identities.