LA30 What is the Inverse of a Matrix?

We define what the inverse of a matrix is, we show that it is unique, and that the product of invertible matrices are invertible. We give examples of invertible and non-invertible matrices, and the general formula for finding the inverse of a 2x2 matrix. The connection with matrix equations and systems of equations is mentioned as a motivation. Subscribe @Shahriari for more undergraduate Math videos.

This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized.

See https://pomona.box.com/s/oahafa797tj5sh55dewyedtys31lamf0 for a complete annotated list of videos for this full course in undergraduate linear algebra

This is also a lecture in a series of lectures on Matrices and their properties. In later videos, we see that Matrices play an important role in Linear Algebra. We use them in the study of vector spaces and, in return, the theory of vector spaces is used to understand matrices.

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA, U.S.A.

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#Maths #Systems_of_Linear_Equations #Linear_Algebra #Matrices #Matrix_Multiplication #Retro_Linear #Pomona_College #Shahriari #Shariari #Iranian-American #Mathematician #Parviz_Shahriari #Iranian #full_course #Inverse #Inverse_of_a_Matrix #Uniqueness_of_Inverses #Product_of_Matrices

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