A community for students.
Here's the question you clicked on:
 0 viewing
Clarence
 one year ago
If A is an invertible matrix then the equation Ax = b may have two distinct non zero solutions for a non zero vector b. True or False?
Clarence
 one year ago
If A is an invertible matrix then the equation Ax = b may have two distinct non zero solutions for a non zero vector b. True or False?

This Question is Closed

clarence
 one year ago
Best ResponseYou've already chosen the best response.1I personally think that it's false, but confirmation is always nice to have.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1why do you think it is false

clarence
 one year ago
Best ResponseYou've already chosen the best response.1If there exist two different solutions, for example Ax1 = Ax2 = b, then A(x1−x2) = 0 with x1 − x2 ≠ 0. Wouldn't that follow up to be saying that there are infinite solutions? If A were invertible, you could write 0 = A^(−1) (0) = A^(−1) (A(x1−x2)) = x1−x2, but that's impossible because x1≠x2, hence A cannot be invertible?

clarence
 one year ago
Best ResponseYou've already chosen the best response.1If that made any sense ~

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1That looks a lot better than what I had : \(A\) is invertible, so \(Ax=b\implies x=A^{1}b\) since the inverse of a matrix is unique (when it exists), the solution is unique.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.