Answered: a = 2 ,8 ,2 ,−2 ,−4 ,−3 ,−11, −4 ,9 ,7…

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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Related questions

Question

a = 2 ,8 ,2 ,−2 ,−4
,−3 ,−11, −4 ,9 ,7

and b = 8,−1

.
SOLVE Ax =b for x , and write x in parametric vector form.

Expert Solution

Step 1: The formation of the system:

$open square brackets table row 2 8 2 cell negative 2 end cell cell negative 4 end cell row cell negative 3 end cell cell negative 11 end cell cell negative 4 end cell 9 7 end table close square brackets open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell row cell x subscript 4 end cell row cell x subscript 5 end cell end table close square brackets equals open square brackets table row 8 row cell negative 1 end cell end table close square brackets L e t space left parenthesis A vertical line b right parenthesis equals open square brackets table row 2 8 2 cell negative 2 end cell cell negative 4 end cell 8 row cell negative 3 end cell cell negative 11 end cell cell negative 4 end cell 9 7 cell negative 1 end cell end table close square brackets A p p l y i n g space v a r i o u s space e l e m e n t a r y space r o w space o p e r a t i o n space o n space space left parenthesis A vertical line b right parenthesis space t o space g e t space i t s space r r e f colon left parenthesis A vertical line b right parenthesis rightwards arrow open square brackets table row 1 4 1 cell negative 1 end cell cell negative 2 end cell 4 row cell negative 3 end cell cell negative 11 end cell cell negative 4 end cell 9 7 cell negative 1 end cell end table close square brackets space comma space R subscript 1 apostrophe equals 1 half R subscript 1 rightwards arrow open square brackets table row 1 4 1 cell negative 1 end cell cell negative 2 end cell 4 row 0 1 cell negative 1 end cell 6 1 11 end table close square brackets comma space R apostrophe subscript 2 equals R subscript 2 plus 3 R subscript 1 rightwards arrow open square brackets table row 1 0 5 cell negative 25 end cell cell negative 6 end cell cell negative 40 end cell row 0 1 cell negative 1 end cell 6 1 11 end table close square brackets comma space R apostrophe subscript 1 equals R subscript 1 minus 4 R subscript 2 H e n c e space t h e space s y s t e m space r e d u c e s space t o x subscript 1 plus 5 x subscript 3 minus 25 x subscript 4 minus 6 x subscript 5 equals negative 40 x subscript 2 minus x subscript 3 plus 6 x subscript 4 plus x subscript 5 equals 11$