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General Mathematics
Matrices
Chapter 4
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RESTS ON
Multiplication and division
FOUNDATIONS
Signed numbers
FOUNDATIONS
Solve a one-step linear equation
FOUNDATIONS
Simplify a fraction
FOUNDATIONS
Convert a percentage to a decimal
CH 1
Percent as parts per hundred
CH 1
Percentage of a quantity
CH 1
Name terms using the chapter's zero-indexed subscript convention
CH 3
Write a recurrence relation as a starting value and a rule
CH 3
Apply the closed rule for the nth term of a geometric sequence
CH 3
Classify sequence behaviour and identify a limiting value
CH 3
Matrix types and order
Matrix addition and subtraction
Scalar multiplication
Matrix products and powers
Inverse matrices and simultaneous equations
Matrices for networks
Transition matrices
State matrices and recurrence
Matrix applications
State the order of a matrix as rows × columns
Address an element by row and column subscripts, in both directions
Classify row, column, square, symmetric and zero matrices
Read a labelled data matrix and its row and column totals
Decide whether a sum or difference of matrices is defined
Add or subtract matrices entry by corresponding entry
Use the zero matrix's behaviour under addition and subtraction
Solve for unknown entries by equating corresponding positions
Multiply every entry of a matrix by a scalar
Evaluate a combination of scalar multiples of two matrices
Test whether a matrix product is defined from the inner numbers
State a matrix product's order from the outer numbers
Multiply matrices by pairing rows with columns and summing the products
Recognise that matrix multiplication is not commutative
Raise a square matrix to a power by repeated multiplication
Use the identity matrix and its unchanged products
Calculate the determinant of a 2 × 2 matrix
Define the inverse as the matrix that multiplies to the identity
Apply the 2 × 2 inverse rule
Recognise that a matrix with determinant zero has no inverse
Write a pair of linear equations as a matrix equation
Solve a matrix equation by left-multiplying by the inverse
Build the connection matrix of a network
Identify the network a connection matrix describes
Link connection-matrix symmetry to two-way connections
Count the connections at a vertex from a row or column sum
Count two-step routes from the square of the connection matrix
Read a transition matrix with columns as the current state
Use the property that every transition-matrix column totals 1
Construct a transition matrix from stated proportions or a diagram
Predict one step ahead from a transition matrix
Write the state matrix as a column indexed by applications
Write the state-matrix recurrence relation
Apply the explicit rule for the state after n steps
Identify the steady state a state sequence settles towards
Set up a matrix product that answers a stated question
Interpret the entries of a matrix product in context
Extract row or column totals with a ones matrix