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I'm thinking of giving up on learning about using the matrix method but maybe I've overlooked some aspect of it?

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- Thread starter rollcast
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- #1

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I'm thinking of giving up on learning about using the matrix method but maybe I've overlooked some aspect of it?

- #2

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- #3

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I'm thinking of giving up on learning about using the matrix method but maybe I've overlooked some aspect of it?

I can guarantee you that solving systems of linear equations with matrix algebra is

Try this: Solve the following system of equations:

3x-y+z-w=0

2x-w+z=2

4x-5y-z=-1

x+y-w=3

a) With substitution or elimination (Your preference)

b) With matrices

Time yourself. It's ok if you give up 20 mins in part a. You're also more likely to make mistakes.

Moral of the post: Matrices exist for a very good reason; they're easy to compute with and faster too. Especially when you have 3+ equations in 3+ unknowns.

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- #4

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Your technique of elimination is essentially Gaussian elimination, but without the benefits of Gaussian elimination. LU decomposition is a step above Gaussian elimination, both in terms of time consumption and stability. QR decomposition is a bit more expensive computationally but has advantages in terms of stability and reusability. There are many other techniques, several of them quite sophisticated because there are lots of ways to get into trouble in solving simultaneous equations.

- #5

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I can guarantee you that solving systems of linear equations with matrix algebra isFARmore efficient than with simple elimination by hand.

Try this: Solve the following system of equations:

3x-y+z-w=0

2x-w+z=2

4x-5y-z=-1

x+y-w=3

a) With substitution or elimination (Your preference)

b) With matrices

Time yourself. It's ok if you give up 20 mins in part a. You're also more likely to make mistakes.

Moral of the post: Matrices exist for a very good reason; they're easy to compute with and faster too. Especially when you have 3+ equations in 3+ unknowns.

I clocked 15 minutes on that and probably made a mistake. touche! haha.

To be honest, when I wrote my response I had assumed that the OP wasn't doing systems of 4 equations.

- #6

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I think I can see the benefit of it now, is their another matrix method other than taking the inverse as it is confusing me a bit and I think that is maybe what is confusing me?

- #7

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Knowing how matrix inversion works is also a first step toward understanding those more advanced techniques. Those more advanced techniques will only make sense if you know the basics of matrix manipulations.

Its a bit like learning to do derivatives using the epsilon-delta formulation. You need to know that formulation to truly understand differentiation. Once you understand it you can pretty much forget it -- until you need to do numerical differentiation of some unknown function. Then it comes in pretty handy.

- #8

HallsofIvy

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