Matrix algebra for beginners, Part I matrices ...

Matrix algebra for beginners, Part Imatrices, determinants, inversesJeremy GunawardenaDepartment of Systems BiologyHarvard Medical School200 Longwood Avenue, Cambridge, MA 02115, January 2006 Contents1 Introduction12 Systems of linear equations13 matrices and Matrix multiplication24 matrices and complex numbers55 Can we use matrices to solve linear equations?66 Determinants and the inverse matrix77 Solving systems of linear equations98 Properties of determinants109 Gaussian elimination1111 IntroductionThis is a Part I of an introduction to the Matrix algebra needed for the Harvard Systems Biology101 graduate course. Molecular systems are inherently many dimensional there are usually manymolecular players in any biological system and linear algebra is a fundamental tool for thinkingabout many dimensional systems.

matrices with capital letters, like A, B, etc, although we will sometimes use lower case letters for one dimensional matrices (ie: 1 ×m or n ×1 matrices). One dimensional matrices are often called vectors, as in row vector for a n ×1 matrix or column vector for a 1 ×m matrix but we are going

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