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?
Interactive exploration
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Connect the picture to the idea(AB)v=A(Bv)(AB)v=A(Bv)

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.

Keep the connection going

One idea leads to another.

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