- #1
SpiffyEh
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Homework Statement
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.
Homework Equations
row reduction
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