System of linear equations

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Stuck on a problem, don't really know how to go about it or what sort of answers it is actually looking for... I got the augmented matrix into RREF and unsure where to go from here. I'm guessing part (a) is when t is any real number except -2. Any advice would be appreciated :-)

(edited 6 years ago)

Reply 1

simon0

Original post by youngar

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For some reason, I can not see the image/question.

Reply 2

youngar

Original post by simon0

For some reason, I can not see the image/question.

Is that any better?

Original post by youngar

Is that any better?

You get a no/infinite solutions when the determinant of that matrix equals 0. What's the determinant of that in terms of

t

? Hence what values of

t

make it zero? Then the answer to part (A) is

t \in \mathbb{R} \setminus \{t_1, t_2\}

for whatever

t_1,t_2

you find as your answers here.

Then you need to consider what happens to your RREF when

t=t_1,t_2

hence deduce which one gives infinite sols and which one gives no sols.

Also, if that RREF correct...?

(edited 6 years ago)

Reply 4

youngar

Original post by RDKGames

You get a no/infinite solutions when the determinant of that matrix equals 0. What's the determinant of that in terms of

t

? Hence what values of

t

make it zero? Then the answer to part (A) is

t \in \mathbb{R} \setminus \{t_1, t_2\}

for whatever

t_1,t_2

you find as your answers here.

Then you need to consider what happens to your RREF when

t=t_1,t_2

hence deduce which one gives infinite sols and which one gives no sols.

Also, if that RREF correct...?

I've tried it again a few times and that's what I keep getting. Though I'm guessing it is incorrect as you can't get the determinant in terms of t...

Reply 5

RDKGames

Study Forum Helper

Original post by youngar

I've tried it again a few times and that's what I keep getting. Though I'm guessing it is incorrect as you can't get the determinant in terms of t...

Huh...?

Well the determinant in terms of

t

is just

\begin{vmatrix} t & 1 & 1 \\ 1 & t & 1 \\ 1 & 1 & t \end{vmatrix}=t[t^2-1]-[t-1]+[1-t]

which can be factorised fully to give two values of

t

for which the system has no unique sols - your RREF does not completely reflect on that, AFAIK.

Reply 6

youngar

Original post by RDKGames

Huh...?

Well the determinant in terms of

t

is just

\begin{vmatrix} t & 1 & 1 \\ 1 & t & 1 \\ 1 & 1 & t \end{vmatrix}=t[t^2-1]-[t-1]+[1-t]

which can be factorised fully to give two values of

t

for which the system has no unique sols - your RREF does not completely reflect on that, AFAIK.

Ohhhh I must be lost off somewhere here cause I thought it was the determinant of the RREF matrix (which is only actually gonna be 1 loool) :colondollar:

my bad. Let me give it another go and I might get back to you if needs be.

Thanks.

(edited 6 years ago)

Reply 7

youngar

@RDKGames

Sorry to be a pain but just wondering how this looks? Supposed to be using the RREF to solve these but thought I'd figure it this way first so I know if I'm heading in the right direction or not. :smile:

Reply 8

DFranklin

No-one ever listens to me on this, but if you have a question like this and it asks you for actual solutions, you might as well simply try to solve the equations (use echelon form etc if you wish), being careful to take note of any places where you might want to divide by 0.

Because yes, there's a nice swish method of using the determinant to find when you don't get a unique solution, but this doesn't actually help you with finding the solutions, so what's the point, really?