Matrices HELP!!!

[astone788]

Need help with this question

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?

[StumbleBum]

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.

[astone788]

Option five has a determinant of 1.

| 1 0 |
| 0 1 |

Where did you get those figures from?

[StumbleBum]

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.
                           

[rife168]

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.

[astone788]

ok. thanks for your help!

[rife168]

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!

[julie9300]

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.

[Yendall]

It doesn't take long to work out determinants on your calculator though.