Matrix arithmetic:
understand the matrix definition and notation
(ACMSM051)
define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and inverse
(ACMSM052)
calculate the determinant and inverse of 2x2 matrices and solve matrix equations of the form AX=B , where A is a 2x2 matrix and X and B are column vectors.
(ACMSM053)
Transformations in the plane:
translations and their representation as column vectors
(ACMSM054)
define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, and the representations of these transformations by 2x2 matrices
(ACMSM055)
apply these transformations to points in the plane and geometric objects
(ACMSM056)
define and use composition of linear transformations and the corresponding matrix products
(ACMSM057)
define and use inverses of linear transformations and the relationship with the matrix inverse
(ACMSM058)
examine the relationship between the determinant and the effect of a linear transformation on area
(ACMSM059)
establish geometric results by matrix multiplications; for example, show that the combined effect of two reflections in lines through the origin is a rotation.
(ACMSM060)