Question

Can someone please explain the matrix method to me with an example? :)

Answer 1

The matrix method of what? Matrices are used for a lot of different things.

Answer 2

Umm hang on, I'll tell you in jusst a minute!

Answer 3

@Kainui Using matrix method, solve the following system of equations:

2/x + 3/y + 10/z = 4, 4/x - 6/y + 5/z = 1, 6/x + 9/y - 20/z = 2; x, y, z is not equal to 0

Answer 4

Ok cool, in fact there are multiple ways we can do this with a matrix. I'll show you with a simpler example:

4a+3b=7
3a-2b=3

So what we do is place everything into a matrix like this: \[\Large \left[\begin{matrix}4 & 3& 7 \\ 3 & -2&3\end{matrix}\right]\] The first column are just the coefficients on our first variable, the next is the coefficients on the second variable, and we'd keep going until we have the stuff it is equal to.

We can now take any row and multiply it by any number. We can also add any row to any other row. And we can interchange rows.

So if I multiply the second row by -1 we get: \[\Large \left[\begin{matrix}4 & 3& 7 \\- 3 & 2&-3\end{matrix}\right]\]Now we can add the bottom row to the top row to get \[\Large \left[\begin{matrix}1 & 5& 4 \\- 3 & 2&-3\end{matrix}\right]\] We can even do multiple rules at a time to save us trouble by just adding a multiple of one row to another. So if I multiply the first row by 3 and add it to the bottom row I get: \[\Large \left[\begin{matrix}1 & 5& 4 \\0 & 17&9\end{matrix}\right]\] Now dividing is really the same as multiplying by a fraction, so there's no problem in dividing the bottom row by 17. \[\Large \left[\begin{matrix}1 & 5& 4 \\0 & 1&9/17 \end{matrix}\right]\] Multiply the bottom row by -5 and add it to the top row to get:\[\Large \left[\begin{matrix}1 & 0& 23/17 \\0 & 1&9/17 \end{matrix}\right]\] and we're almost done!

Now you can rewrite these as equations just like when we converted it into a matrix:

1*a+0*b=23/17
0*a+1*b=9/17

But this is the same as saying

a=23/17 and b=9/17

Cool!

Only difference between what we did here and what you have is you have an extra row and column and your values will be 1/x, 1/y, and 1/z not x, y, and z if this makes sense.

Answer 5

Hang on, ill do this on paper and write down the steps :) gimme like 5 min :)

Answer 6

Yeah take your time, there's a lot there haha.

Answer 7

Haha I understood it, its just like finding the inverse of a matrice(the row and column operations) :) i'll try doing that harder example now :) thanks a ton!

Answer 8

So the idea is to get

One value in A11 or A12 and one value in A21 or A22 so we can easily get the value of a and b, that's the main motive right?