(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given,

A =

[ 1 -3 4;

-3 2 6;

5 -1 -8]

b =

[b_1;

b_2;

b_3]

Show that there does not exist a solution to Ax = b for every b in R3 and describe the set of all {b1,b2,b3} for which Ax = b does have a solution.

2. Relevant equations

row reduction

3. The attempt at a solution

I row reduced until I got the following augmented matrix:

[ 1 -3 4 | b_1;

0 1 (-18/7)| (b_2 + 3*b_1)/7;

0 0 8 | b_3-5*b_1 - 14*b_2]

I'm confused about this because I was lead to believe that since there is a pivot for every value then there should exist a solution for every b in R3. And There is in fact a pivot in every row. Can someone explain to me if there is a solution or not and why please. I'm just not seeing why there wouldn't be one. Thank you

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# Homework Help: Range of a Matrix Transformation linear algebra

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