## Lecture 20: Cramer's rule, inverse matrix, and volume

Now we start to use the determinant. Understanding the cofactor formula allows us to show that *A_ ^{-1} = (1/det_A*)_C_

^{T}, where

*C*is the matrix of cofactors of

*A*. Combining this formula with the equation

*x*=

*A_*gives us Cramer’s rule for solving

^{-1}_b*Ax*=

*b*. Also, the absolute value of the determinant gives the volume of a box.

These video lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook. However, this book is still the best reference for more information on the topics covered in each lecture.

Strang, Gilbert. *Introduction to Linear Algebra*. 5th ed. Wellesley-Cambridge Press, 2016. ISBN: 9780980232776.

**Instructor/speaker:** Prof. Gilbert Strang

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