Function Repository Resource:

# AugmentedMatrix

Get the augmented matrix of the system of linear equations

Contributed by: Dennis M Schneider
 ResourceFunction["AugmentedMatrix"][eqns,vars] returns the augmented matrix of the system of equations eqns in the variables vars.

## Details and Options

Matrix equations or a list of matrix equations are allowed.
If eqns is a list of expressions, then it is assumed that the right-hand sides are 0.

## Examples

### Basic Examples

Find the augmented matrix of a symbolic linear system:

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Matrix equations are allowed:

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When given a list of expressions, AugmentedMatrix assumes that the right-hand sides are 0:

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A mixture of expressions and equations is allowed:

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### Applications

Find all 2×2 matrices whose eigenvectors are (1,2) and (2,-3) :

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Solve the system:

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The resulting matrix is:

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Check that the result satisfies the appropriate eigensystem equation:

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Perform another check to ensure that the eigenvectors are as stated (up to scale):

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