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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
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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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: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
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 >
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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