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- Thread starter Mr Davis 97
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mfb

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Mark44

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Think about the system of equations a matrix represents. A 1x1 matrix represents a single equation such as 3x = 0. For an equation like 3x = 6, you would need an augmented 1x2 matrix. You could solve this by row reduction, but it seems like massive overkill.

A 2x1 matrix would represent a system of two equations in one variable, such as

3x = 0

2x = 0

The matrix itself would consist of a single column whose entries are 3 and 2, respectively. Again, you could use row reduction, and find that (surprise!) x = 0. For such simple systems, you could use RREF, but it doesn't make much sense.

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Mark44

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It would represent a homogeneous system, a system of equations where the constant terms are all zero.

So the system of two equations in one unknown

3x = 0

2x = 0

could be represented by this matrix:

##\begin{bmatrix} 3 \\ 2 \end{bmatrix}##

A nonhomogeneous system such as

4x = 10

2x = 4

could be represented by the augmented matrix

##\begin{bmatrix} 4 & | & 10 \\ 2 & | & 4\end{bmatrix}##

I hope it's obvious that this system has no solution.

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member 587159

That's what I think too.

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chiro

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The algorithm can be applied to an arbitrary matrix since all operations are based on multiplication (scalar multiplication) and addition (and subtraction) which can be done for any set of values.

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mfb

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Mark44

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Most of the linear algebra books I've seen use the matrix for the coefficients of the variables. If the system is nonhomogeneous (constants on the right sides of the equations, they use an augmented matrix.That's what I think too.

If the system of equations is homogeneous, there's no point in dragging along a column of zeroes, none of which can change from any row operations.

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