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. C

Question

2 years ago

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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. C

hoose 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.

Mathematics

1 answer:

rusak2 [61] · Answer 1 · 2022-11-24T10:05:28+03:00

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.