This is your 3x3 matrix, A, to use for this project:
\begin{pmatrix} 9 & 0 & 0 \\ 0 & 2 & 4 \\ 0 & 4 & 2 \end{pmatrix}
Throughout this assignment, all work must be done
alone using the methods as taught in this course.
You must include a selfie holding up your work or
place your id next to your work.
Part I Assignment:
You will be given a matrix, A, as explained above.
(1) Find det(A) using row reduction
(2) Find det(A-\lambda I) using the method of minors and
factor it. To check this plug in \lambda=0 and see if
you get the answer to det(A) that you found in
(2).
(3) Find the eigenvalues of A.
(4) Find the eigenspace for the first eigenvalue of
A and check.
(5) Find the eigenspace for the second eigenvalue
of A and check.
(6) Find the eigenspace for the third eigenvalue of
A and check.
(7) Diagonalize A: find P and D such that AP=PD.
(8) Check the diagonalization using matrix
multiplication: AP=PD
(9) Find the inverse of P and check P times its
inverse is I.
(10) Find the transpose of P. Is it equal to the
inverse of P? Are the columns of P
orthonormal?
Each of these steps is worth ½ a point so that the
total is 5 points.
Do the questions in order
