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(d) Find vectors u, v € R³ such that the solution set of the equation x+y-z = 0 can be written as {su + tv|s, t€ R}.

(d) Find vectors u, v € R³ such that the solution set of the equation x+y-z = 0 can be written as {su + tv|s, t€ R}.

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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Hii, can someone please double check my solutions to this question. If they are incorrect can you please guide me and show me how it should be done. Thank you!!

1. a) x+y+kz=1, x+ky+z=1, kx+y+z=-2

b.) 

The row echelon form is:

1 k 1
0 1-k 0
0 0 -k-2

 

c.) i.) k = -2
ii.) k ≠ -2
iii.) k ≠ 1 and k ≠ -2

d.) not sure, pls help 

Question 1. Consider the augmented matrix of a linear system: k 1 k 1 k 1 1 1 1 -2 (a) Write the system of linear equations corresponding to the given augmented matrix. (b) Find a row echelon form of the given matrix. (c) (i) For what value(s) of k does the system have an infinite number of solutions? Give rea- soning. (ii) For what value(s) of k is the system inconsistent? Give reasoning. (iii) For what value(s) of k does the system have a unique solution? Give reasoning. (d) Find vectors u, v € R³ such that the solution set of the equation x + y − z = 0 can be written {su + tv|s, t € R}. as
Transcribed Image Text:Question 1. Consider the augmented matrix of a linear system: k 1 k 1 k 1 1 1 1 -2 (a) Write the system of linear equations corresponding to the given augmented matrix. (b) Find a row echelon form of the given matrix. (c) (i) For what value(s) of k does the system have an infinite number of solutions? Give rea- soning. (ii) For what value(s) of k is the system inconsistent? Give reasoning. (iii) For what value(s) of k does the system have a unique solution? Give reasoning. (d) Find vectors u, v € R³ such that the solution set of the equation x + y − z = 0 can be written {su + tv|s, t € R}. as
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