A community for students.
Here's the question you clicked on:
 0 viewing
teacherman79
 2 years ago
how do you show the set V of all 2 x 2 upper triangular matrices is a subspace of M22?
teacherman79
 2 years ago
how do you show the set V of all 2 x 2 upper triangular matrices is a subspace of M22?

This Question is Open

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0verify all the conditions for the definition of a subspace, which is really the point of this exercise, to write them down

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0for example, the identity matrix has to be included in the subspace, and \[\begin{pmatrix} 1& 0 \\ 0 & 1 \end{pmatrix}\] is upper triangular, so it is in the subspace

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you have to show it is closed under addition check that \[\begin{pmatrix} a & b \\ c & 0 \end{pmatrix}+\begin{pmatrix} e& f \\ g & 0 \end{pmatrix}\] is upper triangular, which it is etc

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0check that the inverse of an upper triangular two by two matrix is also an upper triangular two by two matrix in other words, write down all the conditions necessary for it to be a subspace, then check them one by one

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2Um, upper triangular 2x2 matrices are matrices of the form \[ \begin{pmatrix} a & b \\ 0 & c \end{pmatrix} \] So some modifications to be made above. Also, the zero vector in \(M_{2 \times 2}\) is the zero matrix, not the identity matrix.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0thanks for keeping me honest

teacherman79
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 @JamesJ Thank you both...this site is cool...wish I knew about it 6 weeks ago...
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.