Full answer: State (with a brief explanation) whether the following statements are true

Chapter 4, Problem 20

(choose chapter or problem)

State (with a brief explanation) whether the following statements are true or false. (a) If the rank of A is n, then A cannot have more than n rows. (b) If matrices A and B are of the same size and k is a scalar, then rank(A) + rank(B) = rank(A + B) and rank(kA) = k rank(A). (c) Consider a system of n equations inn variables. If the matrix of coefficients has rank n, the solution is unique. (d) Ifthe vectorsai. a2, ... , an are linearly dependent then the system of linear equations [a1. a2, ... 'an]x = b has many solutions. (e) Ifthe system oflinear equations[a1, a2, ... 'an]x = b has no solution, then rank([ai. a2, ... , an])