Prove the Matrix has a subspace Watch

NoahMal
Badges: 16
Rep:
?
#1
Report Thread starter 4 weeks ago
#1
I Need help with this question please



Thank you
Last edited by NoahMal; 4 weeks ago
0
reply
NoahMal
Badges: 16
Rep:
?
#2
Report Thread starter 4 weeks ago
#2
Here is what I have so far but im not sure if its correct
0
reply
RichE
Badges: 15
Rep:
?
#3
Report 4 weeks ago
#3
(Original post by NoahMal)
Here is what I have so far but im not sure if its correct
It seems rather confused. What is W, when V is the label of the subspace? Also you need to show two things in V add to give something in V? The matrices you consider aren't in V to begin with, they're general 2x2 matrices.
0
reply
NoahMal
Badges: 16
Rep:
?
#4
Report Thread starter 4 weeks ago
#4
(Original post by RichE)
It seems rather confused. What is W, when V is the label of the subspace? Also you need to show two things in V add to give something in V? The matrices you consider aren't in V to begin with, they're general 2x2 matrices.
How about this? Sorry I mean V misread the question
Attached files
Last edited by NoahMal; 4 weeks ago
0
reply
RichE
Badges: 15
Rep:
?
#5
Report 4 weeks ago
#5
(Original post by NoahMal)
How about this? Sorry I mean V misread the question
Definitely better. You're still calling it W and is your (2,2) entry an "a" or a poorly looking "d"? Should be a "d".
1
reply
NotNotBatman
  • Community Assistant
Badges: 20
Rep:
?
#6
Report 4 weeks ago
#6
So, you'd need to show that v is closed under matrix addition and scalar multiplication.
It's been a while since I've done this, but why have you used w throughout your working instead of v ?

You'd want to say for two matrices in v, the addition is also in v, that is, \begin{pmatrix} a & b\\   c& d \end{pmatrix} + \begin{pmatrix} e & f\\   g& h \end{pmatrix} is in v, which can be shown if you use the condition a+b+c=0 and e+f+g = 0, then you just have (a+e)+(b+f)+(c+g)=0. i.e adding the equations to each other. The second matrix shouldn't have the trailing diagonal as f, as you're making another assumption that these two elements should be equal which isn't a condition given in the question.

Also show why it is closed under scalar multiplication (even if it's obvious).

Then you're good.
1
reply
NoahMal
Badges: 16
Rep:
?
#7
Report Thread starter 4 weeks ago
#7
(Original post by RichE)
Definitely better. You're still calling it W and is your (2,2) entry an "a" or a poorly looking "d"? Should be a "d".
It's A poorly written d

(Original post by NotNotBatman)
.
Thank you
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Edge Hill University
    Undergraduate and Postgraduate - Campus Tour Undergraduate
    Fri, 22 Mar '19
  • Birmingham City University
    Undergraduate Open Day Undergraduate
    Sat, 23 Mar '19
  • University of Bolton
    Undergraduate Open Day Undergraduate
    Sat, 23 Mar '19

Where do you need more help?

Which Uni should I go to? (89)
16.57%
How successful will I become if I take my planned subjects? (55)
10.24%
How happy will I be if I take this career? (96)
17.88%
How do I achieve my dream Uni placement? (81)
15.08%
What should I study to achieve my dream career? (54)
10.06%
How can I be the best version of myself? (162)
30.17%

Watched Threads

View All