Matrices
Size is rows × columns; add entry by entry; a scalar multiplies every entry.
Watch out: rows first.
Revision sheet
All the summary cards of the chapter on one page. Print it, or save it as a PDF from the print window.
Multiplying matrices
(m × n)(n × p) = m × p; entry = row · column.
Watch out: AB is usually not BA.
Determinants and inverses
det = ad − bc; inverse = (1/det)(d, −b; −c, a) when det ≠ 0.
Watch out: the inverse is not the matrix of reciprocals.
Matrices as transformations
Av moves vectors; columns are the images of (1, 0) and (0, 1); areas scale by |det|.
Watch out: the area factor is the determinant, not a sum of entries.
Systems with matrices
AX = B, so X = A⁻¹B when det A ≠ 0.
Watch out: one row per equation; multiply by A⁻¹ on the left.
CC BY-SA 4.0