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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