Given the following vectors: vi =< 1,4,5 >, v2 =< 3, 1,6 >, and v3 =< -2, 1, –2 > Perform the indicated operations to find R¡ and R2. R = 3v, + 2v2 – 5v3 and R2 = 2v, + 4v, – 6v3 Find the constants c1, c2 and c3such that v =c¡Vj+c2V2+c3V3 given that v =< 4,8, 1 >
Given the following vectors: vi =< 1,4,5 >, v2 =< 3, 1,6 >, and v3 =< -2, 1, –2 > Perform the indicated operations to find R¡ and R2. R = 3v, + 2v2 – 5v3 and R2 = 2v, + 4v, – 6v3 Find the constants c1, c2 and c3such that v =c¡Vj+c2V2+c3V3 given that v =< 4,8, 1 >
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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Question
Transcribed Image Text:1 % Given the following vectors: (Encode as column vectors)
2 v1 =
v2 =
4
v3 =
5 %Perform the indicated operations to find R1 and R2.
6.
R1 =
7 R2 =
8 %Find the constants c1,c2 and c3 such that v= c1v1+c2v2+c3v3 given that v=<4 8 1>
9 %Augment the vectors v1,v2 and v3 to form matrix A
10 A =
11
V =
12 %Augment A and v and express as reduced row echelon form.
13 Av =
14 rrefAv =
15 %Extract the column matrix and the remaining matrix
16 Root =
17 AL =
18 if AL ==
eye(size(AL))
c1 = Root(1)
c2 = Root(2)
c3 = Root(3)
19
20
21
22 else
23
display("No Roots Found")
24
c1 = NaN;
25
c2 = NaN;
26
c3 = NaN;
27 end
Transcribed Image Text:Linear Combination
Given the following vectors:
vị =< 1,4,5 >, v2 =< 3, 1,6 >, and v3 =< -2, 1, –2 >
Perform the indicated operations to find R1 and R2.
R1 = 3v, + 2v, – 5v3 and R2 = 2v, + 4v, – 6v3
Find the constants c1, c2 and c3such that v = c¡Vj +c2v2+C3V3 given that v =< 4,8, 1 >
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