Section 6.4 Determinants and Cramer’s Rule

Before Starting this Section, Review

  1. 1 Definition of a matrix (Section 6.1 , page 589)

  2. 2 Systems of equations (Section 5.1 , page 514)

Objectives

  1. 1 Calculate the determinant of a 2×2 matrix.

  2. 2 Find minors and cofactors.

  3. 3 Evaluate the determinant of an n×n matrix.

  4. 4 Apply Cramer’s Rule.

  5. 5 Use determinants in applications.

A Little History of Determinants

It appears that determinants were first investigated in 1683 by the outstanding Japanese mathematician Seki Köwa in connection with systems of linear equations. Determinants were independently investigated in 1693 by the German mathematician Gottfried ...

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