Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Formula Booklet
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AIHL
    /
    Matrices
    /

    Problem Bank

    [Maximum mark: 8]

    In a coastal town, each day is classified as dry (state ​A​) or wet (state ​B).

    Historical records show:

    • If a day is dry, the next day stays dry with probability ​0.4.

    • If a day is wet, the next day stays wet with probability ​0.5.

    1. Determine the transition matrix ​M​ for the daily weather in the town.

      [2]

      To earn a crown, get your answer ready before you reveal the options!

    2. Find the eigenvalues of ​M.

      [4]
    3. Find an eigenvector corresponding to the greater of the two eigenvalues, giving your answer in the form ​(ab​),​ ​a,b∈Z.

      [2]

    Ask Plex AI about this problem

    Get hints, ask questions, and work through this problem step by step

    I'm Plex, here to help with problems on this worksheet!