Specialist Maths Matrices Matrix Arithmetic and Algebra Unit 1 Topic 5 QLD

This powerpoint is on Unit 2 Topic 5: Matrices of the Specialist Maths 2025 Syllabus for QLD. It covers the topic of Matrix arithmetic and algebra and focusses on the following dot points:

•Understand the matrix definition and notation.

•Define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and multiplicative inverse.

•Use matrix algebra properties, including

•A+B=B+A (commutative law for addition)

•A+ 0 =A (additive identity)

•A+(−A)= 0 (additive inverse)

•AI=A=IA (multiplicative identity)

•A(B+C)=AB+AC (left distributive law)

•(B+C)A=BA+CA (right distributive law)

•Recognise that matrix multiplication in general is not commutative.

•Define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and multiplicative inverse.

•Use matrix algebra properties, including

•AA−1=I=A−1A (multiplicative inverse)

•Calculate the determinant and multiplicative inverse of 2×2 matrices, with and without technology.

•If A=[abcd] then det(A)=ad−bc

•A−1=[abcd)]^(-1)=1/(det⁡(A)) [d,-b,-c,a)] , det(A)≠0

•Use matrix algebra to solve matrix equations that involve matrices of up to dimension 2×2, including those of the form AX=B, XA=B and AX+BX=C, with and without technology

•Model and solve problems that involve matrices of up to dimension 2×2, including the solution of systems of linear equations, with and without technology.