Question

Linear Mathematics : Solve the following set of 3 linear equations ?

x+ y - z = 1
2x + 3y + βz = 3
x + βy + 3z =2

For which value of parameter β will the system have

i) Exactly one solution


how do I go about doing this ? Gaussian elimination ?

Answer 1

when beta = -2

Answer 2

this wil give x = y = z = 1

Answer 3

Thanks Jimmyrep, how did you do that please ?

Answer 4

this a pretty important techique that I need to learn, as variations of this question are likely to come up in my exame like
for which value of beta will the system have no solution, many solutions etc

Answer 5

to be honest i just did it by inspection - i thought what if x , y and z were 1 and then plugged 1 into second and third equations to find a common value for beta .
i'd have to think a little more about the technique!

Answer 6

one way would be to let x = y = z and rewrite the equations in x
so first would be 2x- x = 1
x = 1
then plug 1 into equation 2 an3 to find beta

Answer 7

yep - that s the way to go

Answer 8

thanks jimmyrep