7.B-01 Probability vectors

Probability vectors

Build the probability-vector language needed for column-stochastic matrices and Markov models. Begin with normalization and nonnegativity, then interpret conditional transitions and probability mixtures.

What you will practise

• Recognize valid probability columns
• Recover a missing probability
• Interpret destination and source indices
• Combine conditional probabilities

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review fractions, decimals and basic vector notation. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

A final total-probability calculation connects the current state distribution to the next one. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.