3 equations with 3 variables on a Ti-89 Titanium?
Jakob
Is it possible for a Ti-89 Titanium calculator, to solve 3 equations
with 3 variables? If so how does it work?
Solving optimization problems by using the Lagrange method involves
coming up with three equations with three variables (x,y and lambda). I
often get stuck when trying to solve these problems because I cannot
isolate the three variables when the equations are a bit more complex.
But perhaps the calculator can help?
--
Best regards!
Jakob
quasi
If at all possible, don't bother trying to do this on a calculator (it
would be like shoveling snow with a toy shovel).
Instead, use a computer algebra system -- for example, Maple,
Mathematica, or Maxima.
My favorite is Maple, but both Maple and Mathematica cost money,
whereas Maxima is free.
With any computer algebra system you would be able to solve a system
of linear equations exactly and with ease.
If the system is nonlinear, there are methods that can be used to
solve -- for example the Groebner basis method, and although the
computer algebra systems typically have these methods, the process can
be very time consuming.
Can you give an example of the type of system you are trying to solve?
quasi
Michael Varney
www.google.com "how to use google"
www.google.com "linear algebra"
The CAS on a Ti is adequate, but slow as hell. Use Mathematica or
another CAS system.
Also, a better answer of your question depends on the system you are
trying to solve.
jakob
> If the system is nonlinear, there are methods that can be used to
> solve -- for example the Groebner basis method, and although the
> computer algebra systems typically have these methods, the process can
> be very time consuming.
>
> Can you give an example of the type of system you are trying to solve?
Hi!
I'm taking a basic Mathematics course and while you are probably right
that a computer system would be the easiest way, computers are not
allowed for the examination. (algebraic calculators however, are.)
A typical problem could look something like this:
2*x*z=0
2-8*y*z=0
x^2+4*y^2=40
I would probably be able solve it "by hand" and get the solution:
for z=1/4: x=6 and y=1
for z=-1/4: x=-6 and y=-1
But sometimes it is a bit more difficult and if the calculator could
give me the result, I could certainly use that extra time it would give
me, during examination.
--
Best regards
Jakob
quasi
>quasi wrote:
>
>> If the system is nonlinear, there are methods that can be used to
>> solve -- for example the Groebner basis method, and although the
>> computer algebra systems typically have these methods, the process can
>> be very time consuming.
>>
>> Can you give an example of the type of system you are trying to solve?
>
>Hi!
>I'm taking a basic Mathematics course and while you are probably right
>that a computer system would be the easiest way, computers are not
>allowed for the examination. (algebraic calculators however, are.)
>
>A typical problem could look something like this:
>
>2*x*z=0
>2-8*y*z=0
>x^2+4*y^2=40
>
>I would probably be able solve it "by hand" and get the solution:
>
>for z=1/4: x=6 and y=1
>for z=-1/4: x=-6 and y=-1
Your solution is incorrect. Look at the first equation. Doesn't that
show clearly that you made an error? Doesn't equation 1 also suggest a
natural strategy? Hint: equation 1 leads to 2 cases.
This is definitely not a problem for a calculator. Firstly, it's
nonlinear. Secondly, the correct answers may very well involve
radicals which should be represented exactly.
The problem above is clearly testing to see if you understand the
concept of how to solve. It's easily done by hand. It's not a job for
a calculator. A calculator just gets in the way on a problem like
this.
quasi
Ken Oliver
> I'm taking a basic Mathematics course and while you are probably right
> that a computer system would be the easiest way, computers are not allowed
> for the examination. (algebraic calculators however, are.)
>
> A typical problem could look something like this:
>
> 2*x*z=0
> 2-8*y*z=0
> x^2+4*y^2=40
>
> I would probably be able solve it "by hand" and get the solution:
>
> for z=1/4: x=6 and y=1
> for z=-1/4: x=-6 and y=-1
My TI-89 disagrees with your solution:
on the 89 enter:
solve(2*x*z=0 and 2-8*y*z=0 and x^2+4*y^2 = 40, {x,y,z})
hit enter
Note the 'and' from the math/test menu and the curly braces around the
x,y,z
I get x=0 and y =-sqrt(10) and z= -sqrt(10)/40
or
x=0 and y = sqrt(10) and z = sqrt(10)/40
I am not sure how much more complicated the three equations can be and still
have the TI-89 solve it. There must be a limit of some sort.