system of linear equations: { <mtable columnalign="left left" rowspacing=".2em" columns

Hailey Newton

Hailey Newton

Answered question

2022-05-27

system of linear equations:
{ ( 1 + b ) x + y + z = 1 x + ( 1 + b ) y + z = b x + y + ( 1 + b ) z = b 2
And I would like to know if it has zero, one, or more solutions depanding on b ( b R).
How do I do that?

Answer & Explanation

sepolturamo

sepolturamo

Beginner2022-05-28Added 14 answers

Hint: write down the augumented matrix and apply Gaussian elimination to it.
Added: Here is what you should get
[ 1 + b 1 1 1 0 b ( 2 + b ) 1 + b b 1 + b b + b 2 1 1 + b 0 0 ( b + 3 ) b 2 + b b 3 + 2 b 2 b 1 2 + b ] .
Now, you should analyse the last row.
Monserrat Sawyer

Monserrat Sawyer

Beginner2022-05-29Added 3 answers

suppose that b = 0 then you get
x + y + z = 1
x + y + z = 0
x + y + z = 0
clearly it has not solution,of course you can choose different b and test it,or try to reudce it to row echelon form and determine how given system is consistent or has solution.

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