Linear Combination My Solutions Given the following vectors: v =< 1,4,5 >, vy=< 3, 1,6 >, and vy =<-2, 1.-2> Perform the indicated operations to find R, and R,. R, = 3v, + 2v, - Sv, and R; = 2v, + 4v, - 6v, Find the constants c,cz and cysuch that v= cv +cw + cy given that v =< 4,8, 1 > Script o H Save C Reset MATLAB Documentation 1 % Given the following vectors: (Encode as column vectors) 2 v1 - (1; 4; 5] 3 v2 - (3; 1; 6] 4 v3 - [-2; 1; -2) 5 XPerform the indicated operations to find R1 and R2. 6 R1 = 3"v1 + 2"v2 5"v3 % compute R1 7 R2 = 2"v1 + 4"v2 - 6"v3 % compute R2 8 XFind the constants c1,c2 and c3 such that v civ1+c2v2+c3v3 given that v<4 8 1> 9 A- [v1, v2, v3]; 10 y- [4,8.1li

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Linear Combination
My Solutions >
Given the following vectors:
v =< 1,4,5 >, v =< 3,1,6 >, and vy =<-2,1,-2>
Perform the indicated operations to find R, and Ry.
R, = 3v, + 2v, – 5v, and R, = 2v, + 4v - 6v,
Find the constants c,C2 and e;such that v= cv + cv2 + c3v; given that v =< 4,8,1 >
Script e
H Save
C Reset I MATLAB Documentation
1 % Given the following vectors: (Encode as column vectors)
2 vi - [1; 4; 5]
3 v2 - [3; 1; 6]
[-2; 1; -2]
4 v3 =
5 XPerform the indicated operations to find R1 and R2.
6 R1 = 3*v1 + 2"v2 - 5"v3 % compute R1
7 R2 = 2"v1 + 4"v2 - 6"v3 % compute R2
8 XFind the constants c1,c2 and c3 such that v= civi+c2v2+c3v3 given that v=<4 8 1>
9 A = [v1, v2, v3];
10 v - [4,8,1];
11 %Augment the vectors v1,v2 and v3 to form matrix A
12 A =
[v1, v2, v3];
13 v- [4, 8, 1];
14 XAugment A and v and express as reduced row echelon form.
15 Av = [A;v]; % make the augment matrix
16 Ans = rref(Av); %row reduced Av
17 ZExtract the column matrix and the remaining matrix
18 Root = rrefAv(:, end)
19 AL = rrefav(:,1:end-1)
20 if AL eye(size(AL))
21 c1 = Root (1)
22 c2 - Root (2)
23 c3 - Root (3)
24 else
25 display("No Roots Found")
26 c1 = NaN;
27 c2 = NaN;
28 c3 - NaN;
29 end
30 Xverify v value
31 V = c1*v1+c2*v2+c3*v3
Transcribed Image Text:Linear Combination My Solutions > Given the following vectors: v =< 1,4,5 >, v =< 3,1,6 >, and vy =<-2,1,-2> Perform the indicated operations to find R, and Ry. R, = 3v, + 2v, – 5v, and R, = 2v, + 4v - 6v, Find the constants c,C2 and e;such that v= cv + cv2 + c3v; given that v =< 4,8,1 > Script e H Save C Reset I MATLAB Documentation 1 % Given the following vectors: (Encode as column vectors) 2 vi - [1; 4; 5] 3 v2 - [3; 1; 6] [-2; 1; -2] 4 v3 = 5 XPerform the indicated operations to find R1 and R2. 6 R1 = 3*v1 + 2"v2 - 5"v3 % compute R1 7 R2 = 2"v1 + 4"v2 - 6"v3 % compute R2 8 XFind the constants c1,c2 and c3 such that v= civi+c2v2+c3v3 given that v=<4 8 1> 9 A = [v1, v2, v3]; 10 v - [4,8,1]; 11 %Augment the vectors v1,v2 and v3 to form matrix A 12 A = [v1, v2, v3]; 13 v- [4, 8, 1]; 14 XAugment A and v and express as reduced row echelon form. 15 Av = [A;v]; % make the augment matrix 16 Ans = rref(Av); %row reduced Av 17 ZExtract the column matrix and the remaining matrix 18 Root = rrefAv(:, end) 19 AL = rrefav(:,1:end-1) 20 if AL eye(size(AL)) 21 c1 = Root (1) 22 c2 - Root (2) 23 c3 - Root (3) 24 else 25 display("No Roots Found") 26 c1 = NaN; 27 c2 = NaN; 28 c3 - NaN; 29 end 30 Xverify v value 31 V = c1*v1+c2*v2+c3*v3
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