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2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the vectors ( 3;. -2; 1) as a linear combination the e:e and en.

2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the vectors ( 3;. -2; 1) as a linear combination the e:e and en.

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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10 9. 8 7.6. 5 4.131 21 011.12 3.4 5. 6.7 8 10 11 12 13 Activity 1 1. Let x and y be vectors in E". Define x-y as x+(-y). Setting x= ( X1, X2, X3, ... Xn) and y= ( y1,Y2, Y3, ... Yn); Write out the vector x-y 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0);ez = (1; 0; 0); %3D %3D %3D Write down the vectors ( 3;. -2; 1) as a linear combination the e; e2 and e3. 3. Find the constants c, and c2 such that: (3; 5) = C1( 1; -2) +c2( 2; -3) 4. Show that there do not exist constants C1, C2 and c3 which satisfy : (1: -1: 4) = C1( 2; 3; 5) +c2(-1: 0; 6)+c3(1; 3; 11) O dr ENG
Transcribed Image Text:10 9. 8 7.6. 5 4.131 21 011.12 3.4 5. 6.7 8 10 11 12 13 Activity 1 1. Let x and y be vectors in E". Define x-y as x+(-y). Setting x= ( X1, X2, X3, ... Xn) and y= ( y1,Y2, Y3, ... Yn); Write out the vector x-y 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0);ez = (1; 0; 0); %3D %3D %3D Write down the vectors ( 3;. -2; 1) as a linear combination the e; e2 and e3. 3. Find the constants c, and c2 such that: (3; 5) = C1( 1; -2) +c2( 2; -3) 4. Show that there do not exist constants C1, C2 and c3 which satisfy : (1: -1: 4) = C1( 2; 3; 5) +c2(-1: 0; 6)+c3(1; 3; 11) O dr ENG
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