3. Consider the statements below. (I) For each b in Rnı the equation Ax = b has a solution. (II) Each b in R" is a linear combination of the columns of A. (III) The columns of A span Rm. (IV)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 61E
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3.
Consider the statements below.
(I)
For each b in R" the equation Ax = b has a solution.
(II)
Each b in R" is a linear combination of the columns of A.
(III)
The columns of A span Rm.
(IV)
A has a pivot in each row.
Which one of the four statements is not equivalent to the others?
[ 1) I 2) IIT 3) III | 4) IV]
Transcribed Image Text:3. Consider the statements below. (I) For each b in R" the equation Ax = b has a solution. (II) Each b in R" is a linear combination of the columns of A. (III) The columns of A span Rm. (IV) A has a pivot in each row. Which one of the four statements is not equivalent to the others? [ 1) I 2) IIT 3) III | 4) IV]
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