Matrices
Unit 4 is not assessed on the AP exam; schools include it based on local requirements, and matrices lead directly into linear algebra. A matrix is a rectangular array, n rows by m columns in that order. Addition and scalar multiplication act entry by entry, but the product is a row-by-column machine: it demands matching inner dimensions, produces the outer dimensions, and generally gives different answers in different orders.
The mistakes are misrules: reading dimensions columns-first, multiplying entrywise as if the product were addition’s cousin, assuming AB = BA because numbers commute, and multiplying shapes whose inner dimensions never matched. The lesson drills the row-dot-column mechanism until the misrules lose their pull.
The work
3 ways in · any order
Lesson
Matrices
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Rows first, then columns. The lesson locks in dimensions, keeps addition and scalars entrywise, and builds the row-by-column product with its inner-dimension law and its refusal to commute. Ten scenarios close it out: shapes, sums, products, and the orders that fail.
Diagnostic
10-item topic check
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Ten items spanning the Topic 4.10 misconception family: entrywise products, commuted orders, and dimension rules misapplied. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.