Linear algebra Watch

Bameron
Badges: 9
Rep:
?
#1
Report Thread starter 3 weeks ago
#1
Name:  Screen Shot 2019-02-20 at 12.47.01.png
Views: 6
Size:  238.3 KB

Hello, I'm currently doing part b) and getting a little stuck.

My instinct says that I need to write 5 equations, such as x(1) = 2 + s + t and then use the 5 equations to find s, t and then x(1) to x(5)?

However, I'm having real problems eliminating anything... so perhaps I'm not doing what the question is asking?

Or am I meant to be setting x(1) to be 18 (15+2+1) = 2 + s + t?

Also I don't know how I'm to know that there is a unique solution via the inequalities, but I know there is one via the RREF as rk(A) = rk(A|b).

Thanks!!
0
reply
DFranklin
Badges: 18
Rep:
?
#2
Report 3 weeks ago
#2
(Original post by Bameron)
Name:  Screen Shot 2019-02-20 at 12.47.01.png
Views: 6
Size:  238.3 KB

Hello, I'm currently doing part b) and getting a little stuck.

My instinct says that I need to write 5 equations, such as x(1) = 2 + s + t and then use the 5 equations to find s, t and then x(1) to x(5)?
Well, the question explictly tells you to form 5 inequalties, so I'd say your instincts are wrong. (I also have no idea where 2 + s + t came from!).

Your first inequality should be: "Since x_1 = 2 + s - t, and x_1 \geq 0, \, 2 + s - t \geq 0".

For how to proceed after you have the 5 inequalities, you just have to look for ways to find conditions on s and t that eventually allow you to find them.

Spoiler:
Show
It will help to consider the fact that x_2 + x_3 \geq 0
0
reply
Bameron
Badges: 9
Rep:
?
#3
Report Thread starter 3 weeks ago
#3
Ahh I don't know what I'm doing... I've followed your example and completed the other 4 inequalities, but I don't really know what you mean by finding conditions for s and t other than that they are both greater than or equal to 0 and I don't know what using that fact does for me.

Unfortunately your hint of x(2) + x(3) >= 0 hasn't helped me much... x(2) + x(3) = -10t... so -10t >= 0.

(Original post by DFranklin)
Well, the question explictly tells you to form 5 inequalties, so I'd say your instincts are wrong. (I also have no idea where 2 + s + t came from!).

Your first inequality should be: "Since x_1 = 2 + s - t, and x_1 \geq 0, \, 2 + s - t \geq 0".

For how to proceed after you have the 5 inequalities, you just have to look for ways to find conditions on s and t that eventually allow you to find them.

Spoiler:
Show
It will help to consider the fact that x_2 + x_3 \geq 0
Ahh I don't know what I'm doing... I've followed your example and completed the other 4 inequalities, but I don't really know what you mean by finding conditions for s and t other than that they are both greater than or equal to 0 and I don't know what using that fact does for me.

Unfortunately your hint of x(2) + x(3) >= 0 hasn't helped me much... x(2) + x(3) = -10t... so -10t >= 0.
0
reply
DFranklin
Badges: 18
Rep:
?
#4
Report 3 weeks ago
#4
(Original post by Bameron)
Ahh I don't know what I'm doing... I've followed your example and completed the other 4 inequalities, but I don't really know what you mean by finding conditions for s and t other than that they are both greater than or equal to 0 and I don't know what using that fact does for me.

Unfortunately your hint of x(2) + x(3) >= 0 hasn't helped me much... x(2) + x(3) = -10t... so -10t >= 0.
If -10t >=0, what can we say about t? And what else do we know about t? So...
0
reply
Bameron
Badges: 9
Rep:
?
#5
Report Thread starter 3 weeks ago
#5
(Original post by DFranklin)
If -10t >=0, what can we say about t? And what else do we know about t? So...
If -10t>= 0 then t has to be negative to be greater than 0, but we also know t is greater than 0, so we have a contradiction?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#6
Report 3 weeks ago
#6
(Original post by Bameron)
If -10t>= 0 then t has to be negative to be greater than 0, but we also know t is greater than 0, so we have a contradiction?
No, we don't have a contradiction because the inequalities are not strict. t=0 is the only value for which t \leq 0 and t \geq 0 both hold.
0
reply
Bameron
Badges: 9
Rep:
?
#7
Report Thread starter 3 weeks ago
#7
Ok so that leaves me with x(5) = 0, x(2) + x(3) = 0

from x(1), 2+s >= 0 so s >= -2, but from x(4), 4s >= 0, so s>=0, which I already knew from the question.
Last edited by Bameron; 3 weeks ago
0
reply
Bameron
Badges: 9
Rep:
?
#8
Report Thread starter 3 weeks ago
#8
Having s also = 0 give me the correct answer, but I don't know how to prove s = 0 from the other side, just that I know s>=0
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#9
Report 3 weeks ago
#9
(Original post by Bameron)
Having s also = 0 give me the correct answer, but I don't know how to prove s = 0 from the other side, just that I know s>=0
Not sure about s=0 in addition to t=0 ... that would imply x_2 = -4 which is negative.

You can show that s must take on a different specific value though. Notice that the equations for x_2, x_3 are off by a multiple of -1 from each other (after imposing the condition t=0). For them both to be greater than (or equal to) 0, s must take on a specific value which you can determine.
Last edited by RDKGames; 3 weeks ago
0
reply
Bameron
Badges: 9
Rep:
?
#10
Report Thread starter 3 weeks ago
#10
Ok s=4/7 and this give me the correct portion sizes. Thank you both for being so patient with me, I'm going to run through the question again to make sure I understand everything.
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

  • University of Birmingham
    Postgraduate Open Day Postgraduate
    Wed, 20 Mar '19
  • King's College London
    Postgraduate Taught Courses - Arts & Sciences - Strand Campus Postgraduate
    Wed, 20 Mar '19
  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 20 Mar '19

Where do you need more help?

Which Uni should I go to? (35)
14.34%
How successful will I become if I take my planned subjects? (21)
8.61%
How happy will I be if I take this career? (50)
20.49%
How do I achieve my dream Uni placement? (35)
14.34%
What should I study to achieve my dream career? (30)
12.3%
How can I be the best version of myself? (73)
29.92%

Watched Threads

View All