Question

The solution set of Ax=b is the set of all vectors of the form w=p+ v_h, where v_h is any solution of the equation Ax=0.

A. True. The statement accurately describes the solution set.
B. False. The statement does not accurately describe the solution set.
C. True. The solution set is unrelated to the given definition.
D. False. The solution set only involves one vector.

Answer 1

The statement regarding the solution set of Ax=b being the set of all vectors of the form w=p+v_h, where v_h is any solution of Ax=0, is true. This aligns with the principles of linear algebra and the superposition in linear systems. The correct option is B.

Step-by-step explanation:

The statement given in the question, 'The solution set of Ax=b is the set of all vectors of the form w=p+vh, where vh is any solution of the equation Ax=0,' is True.

In linear algebra, given a matrix A and a vector b, the solution set for the equation Ax=b consists of a particular solution p to the equation plus all the solutions of the homogeneous equation Ax=0. This is because the homogeneous equation represents the null space of the matrix A, and adding any vector in this null space to a particular solution returns another solution of the equation Ax=b.

This relationship is a reflection of the principle of superposition in linear systems.