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Systems of Linear Equations
Row reduction, Gaussian elimination, solution structure, rank, and the LU factorization.
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Every homogeneous system
A
x
=
0
A\mathbf{x} = \mathbf{0}
A
x
=
0
always has:
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At least the trivial solution
x
=
0
\mathbf{x} = \mathbf{0}
x
=
0
.
Infinitely many solutions.
Exactly one solution.
No solution when
A
A
A
has more rows than columns.
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