Matrices-back substitution

  • Thread starter TyErd
  • Start date
  • #1
299
0

Homework Statement



I have attached the question

Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?
 

Attachments

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement



I have attached the question

Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?
No, that is not the reason. Look at the final row; it is shorthand for an equation involving x1, x2, x3, x4, x5. What is the equation?

RGV
 
  • #3
299
0
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
 
  • #4
299
0
if the third is also an equation that means there must be an answer right? So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 
  • #5
34,688
6,394
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
For what values of the variables x1, x1, x2, x3, and x4 will this be a true statement?


if the third is also an equation that means there must be an answer right?
Not necessarily. There are three possibilities for a system of equations (which are here represented by an augmented matrix):
1) a unique solution
2) multiple solutions
3) no solution.
So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 

Related Threads on Matrices-back substitution

  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
2
Views
956
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
3
Views
1K
Top