Page 419 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Figure Ex-14

Find a matrix whose nullspace is
15.

(a) a point

(b) a line

(c) a plane

Indicate whether each statement is always true or sometimes false. Justify your answer by giving a
16. logical argument or a counterexample.

(a) If E is an elementary matrix, then A and must have the same nullspace.

(b) If E is an elementary matrix, then A and must have the same row space.

(c) If E is an elementary matrix, then A and must have the same column space.

(d) If does not have any solutions, then b is not in the column space of A.

(e) The row space and nullspace of an invertible matrix are the same.

17. matrices whose nullspace is the line .
(a) Find all

(b) Sketch the nullspaces of the following matrices:

The equation can be viewed as a linear system of one equation in three unknowns.

18. Express its general solution as a particular solution plus the general solution of the corresponding