HL AI – Matrices

Matrix Operations

Markov Chains

Matrix Algebra

Transformations

Eigenvectors

Matrices review

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Learning Outcomes
Understand definition and order of matrices.
Simple operations with matrice: addition, subtraction, scalar multiplying.
Multiplication of matrices.
Identity and zero matrices and determinants of matrices using technology and by hand.
Solving simultaneous equations with matrices and using inverse matrices for solutions.
Understanding eigenvalues and eigenvectors, including diagonalization.
Powers of 2×2 matrices.
Using matrices for transformations.
Determinant of a transformation matrix.
Transition matrices and powers of transition matrices.
Markov chains and initial state probability matrices.
Steady and long term probabilities by continued multiplications.
Describing transformations using translations and finding vectors for translations.
Describing transformations using rotations and finding matrices for rotations, including multiples of 90 degrees, and other degrees (or radians).
Describing transformations using reflections and finding matrices for reflections, including y=0, x=0, y=x, y=-x, and other straight lines such as y=2x.
Describing transformations using stretches and finding matrices for stretches.  Understanding the area of stretches compared with the original.
Describing transformations using enlargements and finding matrices for enlargements.  Understanding the area of stretches compared with the original.