- #1
Cade
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Homework Statement
Suppose you know that the 3 by 4 matrix A has the vector S = (2,3,1,0) as the only special solution to Ax = 0.
(a) What is the rank of A and the complete solution to Ax=0
(b) What is the exact row reduced echelon form R of A?
(c) How do you know that Ax=b can be solved for all b?
Homework Equations
r(A) = n - r
The Attempt at a Solution
a) r(A) = n - r(nullspace) = 4 - 1 = 3
x = a(2,3,1,0), a = any scalar
b) R has 3 pivots and Rx=0 with x = (2,3,1,0)
R = (
(1, 0, -2, 0),
(0, 1, -3, 0),
(0, 0, 0, 1))
c) Clueless. :( How should I attempt this?