Linear Algebra and Probability 3

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. De ne a mapping F : V ! U by
matrix multiplication:
(a) Find the kernel of F:
(b) Find the image of F:
(c) Find the ity of F:
(d) Find the rank of F:
(e) How are the ity and the rank of F related to the dimensions of U and V ?

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