Question

Let A be an m x n matrix and let b be a vector in RM. Three of the following four statements are all equivalent to each other. Choose the one statement that is not equivalent to the other three.
(a) The reduced row echelon form of Ab] has no zero row.
(b) The system Ax = b has a solution.
(c) b can be expressed as a linear combination of the columns of A.
(d) b is in the span of the columns of A.

Answer 1

Answer:

A.

Step-by-step explanation:

From the given information:

If A = m × n matrix

where;

b  is a vector in $R^m$

Then; the statement that doesn't fit and is not related to the other three from the given options is Option A.

This is because the statement in Option A appears to be inconsistent. For the model Ax=b to have a solution, A must be non-singular and b must be in A's column space.

Option c and d are equivalent, also option b and c are equivalent.