Question

1. Consider the following matrix:

(a) A is a ___ × ___ matrix.
(b) rank(A) = _____
(c) Find a basis for the column space of A.
(d) Find a basis for the row space of A.
(e) If A is the coefficient matrix of a homogeneous linear system, find a basis for the solution space of the system.
(f) If A is the coefficient matrix of a non-homogeneous linear system and is the vector on the right-hand side, can be any vector in R3?
(g) If A is the augmented matrix of a linear system, is the system consistent?