Solution Found!
Answer: In Exercises, mark each statement True or False.
Chapter 2, Problem 22E(choose chapter or problem)
Problem 22E
In Exercises, mark each statement True or False. Justify each answer.
a. A subset H of ℝn is a subspace if the zero vector is in H.
b. Given vectors v1,...,vp in ℝn, the set of all linear combinations of these vectors is a subspace of ℝn.
c. The null space of an m × n matrix is a subspace of ℝn.
d. The column space of a matrix A is the set of solutions of Ax = b.
e. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.
Questions & Answers
QUESTION:
Problem 22E
In Exercises, mark each statement True or False. Justify each answer.
a. A subset H of ℝn is a subspace if the zero vector is in H.
b. Given vectors v1,...,vp in ℝn, the set of all linear combinations of these vectors is a subspace of ℝn.
c. The null space of an m × n matrix is a subspace of ℝn.
d. The column space of a matrix A is the set of solutions of Ax = b.
e. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.
ANSWER:
Solution:-
Step1
To find
Mark each statement True or False. Justify each answer.
a. A subset H of ℝn is a subspace if the zero vector is in H.
b. Given vectors v1,...,vp in ℝn, the set of all linear combinations of these vectors is a subspace of ℝn.
c. The null space of an m × n matrix is a subspace of ℝn.
d. The column space of a matrix A is the set of solutions of Ax = b.
e. If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.