Peter Kempthorne of MIT teaches the second lecture in 18.642, Topics in Mathematics with Applications in Finance, laying out linear algebra as a toolkit for quantitative finance. He covers vectors and matrices, then moves into portfolio valuation and the mechanics of short selling, arbitrage, and contingent claims. The second half turns to stochastic matrices and Markov chains and shows how eigenvalues and eigenvectors describe the long run behavior of financial models. The lecture closes on no-arbitrage conditions, market completeness, and pricing measures, the mathematical scaffolding behind option pricing theory. Runtime is about eighty-one minutes, delivered in MIT's standard lecture hall format with the instructor working through notation and derivations at the board. It assumes some comfort with matrix notation and is built for students heading toward option pricing and risk models rather than a general audience.