# Thread: Help With Theoretical MAtrices Question

1. ## Help With Theoretical MAtrices Question

Okay I have two questions that I don't really understand from my textbook, so if somebody could explain them out for me i'd be real grateful.

First, If Ax = b has a solution, explain why the solution is unique precisely when Ax = 0.

Secondly, if b =/= 0 can the solution set of Ax = b be a plane throught the origin?

For the first question I'm not really sure what why its unique, so help would be appreciated.
For the 2nd question I don't think that the solution set of Ax=b can be through the origin because the b values translate it. I'm not sure about this, so someone correct me if I'm wrong.

Again, thanks!

Okay I have two questions that I don't really understand from my textbook, so if somebody could explain them out for me i'd be real grateful.

First, If Ax = b has a solution, explain why the solution is unique precisely when Ax = 0.

== This is false. Choose

(1 0)
(0 0) = A

and column vectors X = (x y)^t , b = (1 0)^t . Then AX = b has the solution (1 0), but the homogeneous system AX = 0 has infinite solutions of the form (0 y), y any real number (I'm assuming you're working with real numbers)

Secondly, if b =/= 0 can the solution set of Ax = b be a plane throught the origin?

No it can't because such a plane contains the zero vector, but when we input this zero vector in the system we get A0 = 0 =/= b .

Tonio

For the first question I'm not really sure what why its unique, so help would be appreciated.
For the 2nd question I don't think that the solution set of Ax=b can be through the origin because the b values translate it. I'm not sure about this, so someone correct me if I'm wrong.

Again, thanks!
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