Please show all work. Thanks! See doc for ma.
Question 1.
Consider the matrix
(a) Find all eigenvalues of A:
(b) For each eigenvalue of A; nd the associated eigenvector(s).
Question 2.
Consider the matrix
(a) Find the determinant of B:
(b) Is B invertible?
Question 3.
Let V be the set of 3 1 matrices and U be the set of 4 1 matrices. Dene a mapping F : V ! U by
matrix multiplication:
(a) Find the kernel of F:
(b) Find the image of F:
(c) Find the nullity of F:
(d) Find the rank of F:
(e) How are the nullity and the rank of F related to the dimensions of U and V ?
