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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: astone788 on October 28, 2012, 03:37:55 pm

Title: Matrices HELP!!!
Post by: astone788 on October 28, 2012, 03:37:55 pm
Need help with this question
(http://i50.tinypic.com/3462t0p.png)
NOTE: the answer is 3. (option 2,3 and 5)
I understand option 2 and 3 have a unique solution because they have a determinant that is NOT zero. But i don't understand why option 5 has a unique solution.
MY prediction is that option 5 has a assumed determinant of 1. Can anyone clarify this?
Title: Re: Matrices HELP!!!
Post by: StumbleBum on October 28, 2012, 03:43:20 pm
Option five has a determinant of 1.

| 1 0 |
| 0 1 |

So the determinant is (1 x 1 - 0 x 0) which equals (1)

Hence it also has a unique solution, along with options 2 and 3.
Title: Re: Matrices HELP!!!
Post by: astone788 on October 28, 2012, 03:44:20 pm
Quote from: StumbleBum on October 28, 2012, 03:43:20 pm
Option five has a determinant of 1.

| 1 0 |
| 0 1 |
Where did you get those figures from?
Title: Re: Matrices HELP!!!
Post by: StumbleBum on October 28, 2012, 03:47:52 pm
The equation would be represented in matrix form by:

| 1 0 | x | x | = | 8 |
| 0 1 |    | y |    | 2 |

So the first matrix | 1 0 | will be what determines the solutions, as it is what we have to take the inverse of. So as it's determinant is 1 there
                           | 0 1 |
will be a unique solution.
                           
Title: Re: Matrices HELP!!!
Post by: rife168 on October 28, 2012, 03:50:29 pm
If you were to set up option 5 as a matrix equation you would get the identity matrix as the coefficient matrix which has a determinant of 1.

For all the options, just find the determinant of the coefficient matrices, if they are non-zero then there is a unique solution.
Title: Re: Matrices HELP!!!
Post by: astone788 on October 28, 2012, 03:52:11 pm
ok. thanks for your help!
Title: Re: Matrices HELP!!!
Post by: rife168 on October 28, 2012, 03:54:11 pm
If you think about it, option 5 should be the most obvious of the choices. Think about what constitutes a unique solution, you have a single value for both x and y. In the case of option 5, you don't even need to do any working out, they simply give you the single values for x and y!
Title: Re: Matrices HELP!!!
Post by: julie9300 on October 30, 2012, 11:34:28 am
I think using matrices would be wasting a bit a time to find whether or not there's a unique solution. A unique solution pretty much means that two linear functions intersect with one another and so for that to happen, the two functions cannot have the same gradient. x=8 has an undefined gradient and y=2 has a gradient of 0. Even without looking at the gradients, you can tell that those two lines will intersect at (8,2) and since they intersect they therefore have a unique solution.
Title: Re: Matrices HELP!!!
Post by: Yendall on October 30, 2012, 12:16:06 pm
It doesn't take long to work out determinants on your calculator though.