- Mathematics General
- Year 12
Matrices
approx. 15 hrs
2 topics
40 concepts
Deepen your understanding of Matrices and the skills to approach your examinations with confidence.
approx. 15 hrs
2 topics
40 concepts
Deepen your understanding of Matrices and the skills to approach your examinations with confidence.
Year 12 Matrices is a learning program that covers the essential components of Year 12 General Mathematics and is aligned with the Australian curriculum. As part of this course, students develop their ability to conduct mathematical operations with matrices, and to apply matrices to solve practical problems, including the use of permutation, communication and dominance matrices.
This learning program is made up of the following 2 topics, broken down into 40 concepts.
Construct a matrix to represent connections of a network diagram
Construct a network diagram from a matrix
Find the determinant of a 2x2 matrix
Find the inverse of a 2x2 matrix
Evaluate matrix expressions involving powers
Application of permutation matrices
Construct a communication matrix from a diagram
Construct a dominance matrix
Application of binary matrices to model and solve a range of word problems
Find the determinant and the inverse of an nxn matrix using a calculator
Using the determinant test to identify simultaneous equations with no solution
Construct a transition matrix from a transition diagram
Interpreting a transition matrix
Construct a matrix recurrence relation
Use a recursion relation to calculate state matrices step-by-step
Determine the nth state of a system
Estimate the steady state solution
Use of powers of matrices to model and solve word problems
Solve simultaneous equations using application of inverse matrices
Determine the transpose of a matrix
Use a matrix to represent data tables
Application of matrices to solve a range of word problems
Use matrices to encode a message
Use matrices to decode a message
Solve simultaneous equations using matrices on a CAS calculator
Multiply two matrices using a calculator
Use of a rule for the aijth element of a matrix to construct the matrix
Use summing matrices to sum the rows and columns of matrices
Multiply two matrices
Determine the order of a matrix product
Add matrices
Subtract matrices
Perform scalar multiplication of a matrix
Calculate the sum of elements in a row or column
Identify the elements in a matrix using notation
Use the matrix template of the calculator to retrieve values of elements
Identify different types of matrices including row, column, square, identity, diagonal, triangular, symmetric and zero
Perform a combination of addition, subtraction and scalar multiplication of matrices
Use a calculator to perform operations with matrices
Write down the order of a matrix
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