VCE Methods Question Thread!

[Hutchoo]

Just a few quick questions:
Is there any benefit in solving 3 simultaneous equations via the matrix method?

I was doing a question (see attached) that made me a bit confused in regards to my CAS (the question was easy, but I wanted to see how I could do it in my CAS). Anywhhooooo, I was letting A, B and C equal their respective matrix and I put it in the CAS as: AX + B  = C, solve X, but it didn't work. Am I overestimating the capability of my CAS, or can it solve things like that?

Thanks.

[Panicmode]

Just a few quick questions:
Is there any benefit in solving 3 simultaneous equations via the matrix method?

I was doing a question (see attached) that made me a bit confused in regards to my CAS (the question was easy, but I wanted to see how I could do it in my CAS). Anywhhooooo, I was letting A, B and C equal their respective matrix and I put it in the CAS as: AX + B  = C, solve X, but it didn't work. Am I overestimating the capability of my CAS, or can it solve things like that?

Thanks.

You have to define each of the matrices as the present variable, then you have to input a matrix x which has unknown variables. It should then solve. I used a classpad though (yes, sue me) so not sure how it works on the others.

[Hutchoo]

Just a few quick questions:
Is there any benefit in solving 3 simultaneous equations via the matrix method?

I was doing a question (see attached) that made me a bit confused in regards to my CAS (the question was easy, but I wanted to see how I could do it in my CAS). Anywhhooooo, I was letting A, B and C equal their respective matrix and I put it in the CAS as: AX + B  = C, solve X, but it didn't work. Am I overestimating the capability of my CAS, or can it solve things like that?

Thanks.

You have to define each of the matrices as the present variable, then you have to input a matrix x which has unknown variables. It should then solve. I used a classpad though (yes, sue me) so not sure how it works on the others.

What do you mean by present variable?

[Panicmode]

Just a few quick questions:
Is there any benefit in solving 3 simultaneous equations via the matrix method?

I was doing a question (see attached) that made me a bit confused in regards to my CAS (the question was easy, but I wanted to see how I could do it in my CAS). Anywhhooooo, I was letting A, B and C equal their respective matrix and I put it in the CAS as: AX + B  = C, solve X, but it didn't work. Am I overestimating the capability of my CAS, or can it solve things like that?

Thanks.

You have to define each of the matrices as the present variable, then you have to input a matrix x which has unknown variables. It should then solve. I used a classpad though (yes, sue me) so not sure how it works on the others.

What do you mean by present variable?

Sorry, that was 2 o'clock brain talking. I meant to say each variable present in the equation.


EDIT:

Alternately though you might find it easier to just define variables A, B and C, then solve the letter equation by hand, input it into the calc and voila!

eg. AX + B = C

X = A^-1(C-B)

If you input A^-1(C-B) into the calc it should come up with the correct matrix X.

[Bhootnike]

i think this is a silly question, but how do you divide a polynomial , by say ,
the factors would be yea?

i tried synethetic division on the question i was doing initially, and it didnt really work out :s
or would this be a genuine calc question?

[dc302]

i think this is a silly question, but how do you divide a polynomial , by say ,
the factors would be yea?

i tried synethetic division on the question i was doing initially, and it didnt really work out :s
or would this be a genuine calc question?

edit: sorry totally misread your question. To divide it by that, normal long division will work.

[Bhootnike]

i did it normally and got the answer, - what was happening was that i did every question in the exercise by synthetic division, and for this one i got stuck. so pretty much, dont do these by synthetic?

[dc302]

i did it normally and got the answer, - what was happening was that i did every question in the exercise by synthetic division, and for this one i got stuck. so pretty much, dont do these by synthetic?

I don't know if this is true but my teachers used to say that synthetic wasn't 'appropriate maths' to use in an exam so I never used it.

[Bhootnike]

well i figured you can't use it with complex numbers , so no for spesh,
but in methods is pretty good , except for when dividing by e.g.

i guess you can't do it synthetically then :p !

[Hutchoo]

Just a few quick questions:
Is there any benefit in solving 3 simultaneous equations via the matrix method?

I was doing a question (see attached) that made me a bit confused in regards to my CAS (the question was easy, but I wanted to see how I could do it in my CAS). Anywhhooooo, I was letting A, B and C equal their respective matrix and I put it in the CAS as: AX + B  = C, solve X, but it didn't work. Am I overestimating the capability of my CAS, or can it solve things like that?

Thanks.

You have to define each of the matrices as the present variable, then you have to input a matrix x which has unknown variables. It should then solve. I used a classpad though (yes, sue me) so not sure how it works on the others.

What do you mean by present variable?

Sorry, that was 2 o'clock brain talking. I meant to say each variable present in the equation.


EDIT:

Alternately though you might find it easier to just define variables A, B and C, then solve the letter equation by hand, input it into the calc and voila!

eg. AX + B = C

X = A^-1(C-B)

If you input A^-1(C-B) into the calc it should come up with the correct matrix X.

Yeah, I did it like that.
Anyway, can someone please answer my first question
ty

[Shenz0r]

I've got a few questions:

1. Let P(x) = x⁵ - 3x⁴ + 2x³ - 2x² + 3x +1.
Given that P(x) can be written in the form (x² - 1)Q(x) + ax + b, where Q(x) is a polynomial and a and b are constants, hence or otherwise, find the remainder when P(x) is divided by x² - 1.

Answer is 6x - 4.

2. Divide x⁴ - 9x³ + 25x² - 8x -2 by x² - 2.

3. Without using a calc, find the equation of a third-degree polynomial which passes through (1,1) (3,4) (0,0) and (-2,-4). I keep screwing up my algebra.

4. A parabola passes through the points (a,0) (b,0) and (1,1). Find its equation and hence state any restrictions on a and b.

[brightsky]

1. x^5 - 3x^4 + 2x^3 - 2x^2 + 3x + 1 = (x^2-1)Q(x) + ax + b
x^5 - 4x^4 + 2x^3 - 2x^2 + (3-a)x + (1-b) = (x^2 - 1)Q(x)
now let A(x)=x^5 - 4x^4 + 2x^3 - 2x^2 + (3-a)x + (1-b) for convenience's sake.
since x^2 -1 is a factor of A(x), x - 1 and x+1 are factors
so
A(1) = 0
A(-1)=0
now solve simultaneously to get a and b, which should be 6 and -4 respectively.

2. standard polynomial division question. just ake sure that you write x^2 - 2 as x^2 + 0x - 2 when you're performing the division.

3. i remember answering this exact question on this forum a few days ago. it might even be on this thread.

4. i've answered this too. search around.

[Bhootnike]

I've just done those too haha

[Zahta]

was just wondering in matrices if you have to answer a question with no solution , the det is =0 right so  infinetly many solutions. So  i have a  question that is part a no solution and then part b infinitely many solution. Wouldn't you get same answer  because your making det =0  why is der part a and b for that question


confused. please help anyone

[TrueTears]

Note that when the determinant of a matrix is 0 it could mean that it has no solutions or infinitely many solutions. To find out which, you could reduce the matrix down to its reduced row echelon form (http://en.wikipedia.org/wiki/Row_echelon_form).