Question

Linear algebra! Trying to construct a 3x3 matrix so that Ax=(1,2,1) has no solutions, but Ax=(1,0,1) and Ax=(1,1,0) both have infinite solutions

Answer 1

My book does not really ever explain how to construct a matrix like this. There isn't even a practice question like it.

All I can figure (I think this is right) is that 1,2,1 is not in the columnspace of A and the other two vectors are. Also I think rank(A)<m and rank(A)<n (so rank(A)<3. And the nullspace must have nonzero vectors

Answer 2

Erm, i understand matrix, but i dont do them a lot. so i don;t understand your notations like Ax= (1,2,1). I have no idea wat is the question, kindly elaborate thx.

Answer 3

You're on track so far. You know two of the columns of the matrix, can you determine the third? You are correct in saying that it can't be linearly independent of the other two, which should make it pretty easy...

Answer 4

Just to clarify slightly, there are an infinite number of possibilities but there is a particular option that is staring you in the face.

Answer 5

hmm, well It has been staring me in the face for 6 hours, and I have class in 5! haha.

Answer 6

AH! GOT IT. THANKS A LOT. I feel stupid but really the textbook could have added one sentence that would have saved me 6 hours when all I had to do was add the damn things!

Answer 7

:)