Further Maths - Matrices

describe the identity matrix

1s on leading diagonal (top left to bottom right) 0s everywhere else

Transpose

switch the rows and columns (superscript T)

Describing matrix dimensions

down then right (number of rows x number of columns)

conformable

can be multiplied (Left matrix columns = right matrix rows)

commutative

operation that gives the same result regardless of order (a+b = b+a)

associative

grouping doesn’t matter ( A(BC) = (AB)C)

determinant of a 2×2 matrix

ad-bc

For 2×2 matrices, detAB = detBA =

detA x detB

det(kA) =

k²detA

A multiplied by what matrix is I?

A^-1

singular matrix has the property ___ and has no ___

determinant = 0, inverse

formula for inverse of 2×2 matrix

A^-1 = 1/detA(d -b next row: -c a)

(AB)^-1 =

B^-1 x A^-1