Random Q's for exam...

[stonecold]

Unless a question asks for an answer in a specific form, say for a derivative, we can't get docked marks can we?

I know numerical answers must be in simplest form...

[stonecold]

Also, for trig general solutions, is it best to just stick to the ranges / formulas in the essentials book?

[lovingit]

What does it mean if the determinate of a matrix is negative

[stonecold]

What does it mean if the determinate of a matrix is negative

that unique solutions exist, same as if it is positive.

it is when it = 0, the matrix is singular, meaning that either none or infinite solutions exist.

[lachymm]

I havent learnt how to do them by matrice's is it still ok to just know the other way ?

[stonecold]

I havent learnt how to do them by matrice's is it still ok to just know the other way ?

unless it says using matrices...

[Souljette_93]

I havent learnt how to do them by matrice's is it still ok to just know the other way ?

me too..it's easier the other way. And you can do it another way, so long you get the answer.

Stonecold: can you explain how to do it by matrix?

[stonecold]

It is the same thing really.

say you have 2x + my = 4  and 5x + 9y = 10, then you set it up as matrices, and solve the determinant to equal 0.

| 2  m |
|        |  = 0
| 5  9 |

2(9) - 5m = 0
5m =18
m=18/5

then you gotta sub you m values back in to see whether it gives infinite solutions or no solutions...

[lachymm]

For the people who havent learnt the binomial theorem check this out: http://www.youtube.com/watch?v=Cv4YhIMfbeM&p=E88E3C9C7791BD2D&playnext=1&index=12

[kenhung123]

We need need to rationalise denominators and put answers over a common denominator?

When doing general solutions? I don't think so, i never do.

Umm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?

[stonecold]

We need need to rationalise denominators and put answers over a common denominator?

When doing general solutions? I don't think so, i never do.

Umm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?

yeah, try not to have square roots on the bottom...

[lachymm]

| 2  m |
|        |  = 0
| 5  9 |



but how do you know what values of m correspond to a unique, no or infinite solutions?

[stonecold]

| 2  m |
|        |  = 0
| 5  9 |



but how do you know what values of m correspond to a unique, no or infinite solutions?

Sub them back into your equation(s)

If you get two identical equations, then there are infinite solutions.  And note x+y=1 and 2x+2y=2 are identical etc.
If you get two different equations, which will have the same gradient but a different y-intercept, then there are no solutions, as they are parallel lines which will never intersect.

[kenhung123]

We need need to rationalise denominators and put answers over a common denominator?

When doing general solutions? I don't think so, i never do.

Umm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?

yeah, try not to have square roots on the bottom...

Thanks

[Blakhitman]

The reasoning behind the determinant thing is because if you recall solving by matrices, AX=B you multiply A^-1 by B to find X.

To get the inverse of a (2x2) matrix:

Notice the determinant in the denominator? well if it doesn't equal zero then is defined and will give one (unique) value so there is one solution. however if it equals 0 then there are no (or infinite) solutions.