The following problems all reference a, but are not all related to each other.

(a) put a in row-reduced echelon form.
(b) viewing a as an augmented matrix, write down the system of linear equations a describes.
(c) viewing a as an augmented matrix, is the associated linear system consistent? if so, write down its solution set.
(d) write down the homogeneous system of linear equations a describes.
(e) find all solutions to this homogeneous system.
(f) give a basis for the solution space. what is its dimension?
(g) find an orthonormal basis for the solution space.
(h) find the determinant of a using

(i) cofactor expansion and
(ii) row reduction.

(i) is a invertible? why or why not? if so, compute a−1 .
(j) write down the characteristic polynomial for a.