[Verse 1]
Variables dance in single file
No squares or cubes, just clean and straight
First power only, that's our style
Linear equations don't complicate
When letters meet with constants true
A-sub-one x plus A-sub-two
[Chorus]
Matrix A times vector x equals b
Three row moves set variables free
Swap them, scale them, add one to another
Gaussian magic makes solutions clearer
Pivot down and eliminate
Watch the zeros calculate
[Verse 2]
Stack equations in a grid
Coefficients form a wall
Augmented matrix can't stay hid
Row echelon answers the call
Leading entries march right down
Zeros underneath don't make a sound
[Chorus]
Matrix A times vector x equals b
Three row moves set variables free
Swap them, scale them, add one to another
Gaussian magic makes solutions clearer
Pivot down and eliminate
Watch the zeros calculate
[Bridge]
One solution when pivots count to n
Infinity when pivots fall behind
No solution when contradictions blend
Zero row with constants undefined
R-E-F or R-R-E-F
Reduced form makes checking less complex
[Verse 3]
Organized reduction clears the fog
Algorithm backbone standing strong
Each elimination breaks the log
Variables surrender one by one
Consistency determines the way
Unique or infinite or no display
[Chorus]
Matrix A times vector x equals b
Three row moves set variables free
Swap them, scale them, add one to another
Gaussian magic makes solutions clearer
Pivot down and eliminate
Watch the zeros calculate
[Outro]
Linear systems tell their tale
Through elimination's ancient trail
Pivots guide us to the end
Where mathematics and logic blend