Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`LinearAlgebraPaclet`
ConsistentMatrixQ  |
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Details and Options
Examples
(1)
Basic Examples
(1)
Determine if an augmented matrix represents a consistent linear system of equations:
In[1]:=
 | ConsistentMatrixQ |
1 | 7 | 3 | -4 |
0 | 1 | -1 | 3 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | -2 |
Out[1]=
False
The reduced row echelon form contains a contradiction that so the matrix is not consistent:
0+0+0=1
x
1
x
2
x
3
In[2]:=
RowReduce
//MatrixForm
1 | 7 | 3 | -4 |
0 | 1 | -1 | 3 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | -2 |
Out[2]//MatrixForm=
1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 0 | 0 | 1 |
The solution set is empty. No solutions exist:
In[3]:=
LinearSolveMap[Most]
(*thecoefficientmatrix*),Map[Last]
(*therightmostcolumn*)
1 | 7 | 3 | -4 |
0 | 1 | -1 | 3 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | -2 |
1 | 7 | 3 | -4 |
0 | 1 | -1 | 3 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | -2 |
Out[3]=
LinearSolve[{{1,7,3},{0,1,-1},{0,0,0},{0,0,1}},{-4,3,1,-2}]
In[4]:=
eqns={+7+3-4,-3,0+0+01,-2};
x
1
x
2
x
3
x
2
x
3
x
1
x
2
x
3
x
3
In[5]:=
Solve[eqns,{,,}]
x
1
x
2
x
3
Out[5]=
{}
The augmented matrix of a linear system is given below. Determine if the system is consistent:
In[6]:=
| ConsistentMatrixQ |
1 | 5 | 2 | -6 |
0 | 4 | -7 | 2 |
0 | 0 | 5 | 0 |
Out[6]=
True
 |
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""