Consider the system of linear equations: { x + a y = 1 b x...

Mohamed Mooney

Mohamed Mooney

Answered

2022-06-28

Consider the system of linear equations:
{ x + a y = 1 b x + 5 y = 2 ,
where a and b are parameters.
(a) Determine the conditions on a and b to get a unique solution.
(b) Determine the conditions on a and b to get infinitely many solutions.
(c) Determine the conditions on a and b such that the system has no solutions.

Answer & Explanation

laure6237ma

laure6237ma

Expert

2022-06-29Added 27 answers

a) a b 5
The determinant of the matrix not equal to zero. There is a unique solution
b) a = 5 2 , b = 2
The determinant is zero, but the two lines are identical, There are infinitely many solution
c) a b = 5 ¬ ( a = 5 2 b = 2 )
The determinant is zero, but the two lines are parallel. There are no solutions
The determinant ( 5 a b )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

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

Didn't find what you were looking for?