The columns of an invertible n times n matrix form a basis f

The columns of an invertible n times n matrix form a basis for R^n. b. The column space of an m times n matrix is a subspace of R^m. c. The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of R^n. d. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for the column space of A. e. The null space of an m times n matrix is a subspace of R^m.

Solution

a) True ( The column of an invertible nxn matrix form a basis for Rⁿ)

b) True ( The column space of an mxn matrix is a subspace of R^m)

c) False

d) False. It is the corresponding columns in A

e) True