V (,474) W: (4,6,6) MAT111 MATHCAFE (Homework for Friday's session - 16/4] Each of you must look for (or create) THREE vectors of R' (i.e. vectors with three components) where one of the vectors, name it w, is a linear combination of the other two, name them u and v. This means you must show that taking a general linear combination u and v equal to w will give you a consistent system. HINT: Cheat a little and use the first two vectors u and v to deduce a vector w so that you will be sure to give the correct vectors. e.g. I propose that my u = (1,2,-1) and v = (3,0,-1) and I claim that w = (5,4,-3) is a linear combination of u and v. Why am I confident with this claim? Well, 2(1,2,-1) + 1(3,0,-1) = (5,4,-3). Warning: You are not allowed to propose vectors with more than one zero in the component similar to the standard basis (we will see this this week), e.g. u = (2,0,0), v = (0,3,0), w=. IS NOT ALLOWED! two components are zero See slides 4, 5 & 6 of Lecture 9 for an example of what you need to do for the solution; but note that that example is on vectors of R', so in your case you will get 3 equations. What you need to give me is u, v, and w and post it in the whatsapp group. i.e. u = L,_),v=L,_), w= L,__) Write or type your solution and save it on the computer as an image or pdf to be shared and presented in the session. Reminder: Please do not just give me any three vectors without checking their relation (see Hint above)! -Dr. Hajar
V (,474) W: (4,6,6) MAT111 MATHCAFE (Homework for Friday's session - 16/4] Each of you must look for (or create) THREE vectors of R' (i.e. vectors with three components) where one of the vectors, name it w, is a linear combination of the other two, name them u and v. This means you must show that taking a general linear combination u and v equal to w will give you a consistent system. HINT: Cheat a little and use the first two vectors u and v to deduce a vector w so that you will be sure to give the correct vectors. e.g. I propose that my u = (1,2,-1) and v = (3,0,-1) and I claim that w = (5,4,-3) is a linear combination of u and v. Why am I confident with this claim? Well, 2(1,2,-1) + 1(3,0,-1) = (5,4,-3). Warning: You are not allowed to propose vectors with more than one zero in the component similar to the standard basis (we will see this this week), e.g. u = (2,0,0), v = (0,3,0), w=. IS NOT ALLOWED! two components are zero See slides 4, 5 & 6 of Lecture 9 for an example of what you need to do for the solution; but note that that example is on vectors of R', so in your case you will get 3 equations. What you need to give me is u, v, and w and post it in the whatsapp group. i.e. u = L,_),v=L,_), w= L,__) Write or type your solution and save it on the computer as an image or pdf to be shared and presented in the session. Reminder: Please do not just give me any three vectors without checking their relation (see Hint above)! -Dr. Hajar
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:V (,474)
W: (4,6,6)
![MAT111 MATHCAFE (Homework for Friday's session - 16/4]
Each of you must look for (or create) THREE vectors of R' (i.e. vectors with three components) where
one of the vectors, name it w, is a linear combination of the other two, name them u and v. This means
you must show that taking a general linear combination u and v equal to w will give you a consistent
system.
HINT: Cheat a little and use the first two vectors u and v to deduce a vector w so that you will be sure
to give the correct vectors.
e.g. I propose that my u = (1,2,-1) and v = (3,0,-1) and I claim that w = (5,4,-3) is a linear combination
of u and v. Why am I confident with this claim? Well, 2(1,2,-1) + 1(3,0,-1) = (5,4,-3).
Warning: You are not allowed to propose vectors with more than one zero in the component similar
to the standard basis (we will see this this week), e.g. u = (2,0,0), v = (0,3,0), w=.
IS NOT ALLOWED!
two components are zero
See slides 4, 5 & 6 of Lecture 9 for an example of what you need to do for the solution; but note that
that example is on vectors of R', so in your case you will get 3 equations.
What you need to give me is u, v, and w and post it in the whatsapp group.
i.e. u = L,_),v=L,_), w= L,__)
Write or type your solution and save it on the computer as an image or pdf to be shared and
presented in the session.
Reminder: Please do not just give me any three vectors without checking their relation (see Hint
above)!
-Dr. Hajar](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e75ff13-537e-48c1-b338-b1d9f455e12e%2F4b87415d-2b8c-4dfb-9dea-cd90da8efc7e%2Fail90hh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:MAT111 MATHCAFE (Homework for Friday's session - 16/4]
Each of you must look for (or create) THREE vectors of R' (i.e. vectors with three components) where
one of the vectors, name it w, is a linear combination of the other two, name them u and v. This means
you must show that taking a general linear combination u and v equal to w will give you a consistent
system.
HINT: Cheat a little and use the first two vectors u and v to deduce a vector w so that you will be sure
to give the correct vectors.
e.g. I propose that my u = (1,2,-1) and v = (3,0,-1) and I claim that w = (5,4,-3) is a linear combination
of u and v. Why am I confident with this claim? Well, 2(1,2,-1) + 1(3,0,-1) = (5,4,-3).
Warning: You are not allowed to propose vectors with more than one zero in the component similar
to the standard basis (we will see this this week), e.g. u = (2,0,0), v = (0,3,0), w=.
IS NOT ALLOWED!
two components are zero
See slides 4, 5 & 6 of Lecture 9 for an example of what you need to do for the solution; but note that
that example is on vectors of R', so in your case you will get 3 equations.
What you need to give me is u, v, and w and post it in the whatsapp group.
i.e. u = L,_),v=L,_), w= L,__)
Write or type your solution and save it on the computer as an image or pdf to be shared and
presented in the session.
Reminder: Please do not just give me any three vectors without checking their relation (see Hint
above)!
-Dr. Hajar
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