Linear Algebra · Advanced · 5 min
Composing matrices
Matrix multiplication represents composition in the order that the transformations act.
WHAT HAPPENS IF…Which matrix acts first in ABv?
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A rotates the plane, while B stretches the horizontal coordinate. A stretch along the original x-axis and one after rotation need not act along the same geometric direction. For a quarter-turn and stretch factor 2, (AB)(1,2)=(−2,2), but (BA)(1,2)=(−4,1).
A detail that matters
Matrix multiplication is generally not commutative.
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