Find the values for k that make this system: - Inconsistent (no solutions) - With unique so

Jamiya Weber

Jamiya Weber

Answered question

2022-06-25

Find the values for k that make this system:
- Inconsistent (no solutions)
- With unique solution
- With infinite solutions
{ k x + y + z = 1 x + k y + z = 1 x + y + k z = 1

Answer & Explanation

aletantas1x

aletantas1x

Beginner2022-06-26Added 22 answers

Hints: The determinant is:
k 3 3 k + 2 = ( k 1 ) 2 ( k + 2 ) = 0 k = 1 , 2
We want the determinant to be nonzero for unique solutions.
If we substitute k = 1 in the system, and do a RREF we have:
( 1 1 1 1 0 0 0 0 0 0 0 0 )
If we substitute k = 2 in the system, and do a RREF we have:
( 1 0 1 0 0 1 1 0 0 0 0 1 )
Can you now derive conclusions for inconsistent, unique solution and infinite solutions?
Davion Harding

Davion Harding

Beginner2022-06-27Added 4 answers

Firstly, if the determinant is not zero, then you have unique solutions. if the determinant is zero however

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?