Matrix Multiplication (VCE SSCE General Mathematics): Flashcards

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Matrix Multiplication
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Dimension rule for matrix multiplication

Columns in 1st must equal rows in 2nd

Order of ABAB when AA is m×nm \times n, BB is n×pn \times p

m×pm \times p

Matrix multiplication commutativity

Not commutative; generally ABBAAB \neq BA

Identity matrix II structure

1s on diagonal, 0s elsewhere (square matrix)

Identity matrix property with any matrix AA

AI=A=IAAI = A = IA

Meaning of A2A^2

A×AA \times A

Which matrices can be raised to a power

Only square matrices

Run and dive method

Run along rows of 1st, dive down columns of 2nd

What matrix multiplication combines

Rows from 1st matrix with columns from 2nd

Notation for multiplying matrix AA by matrix BB

A×BA \times B or ABAB

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