Cramer's Rule, Inverse Matrix and Volume

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

Now we start to use the determinant. Understanding the cofactor formula allows us to show that A-1 = (1/detA)CT, where C is the matrix of cofactors of A. Combining this formula with the equation x = A-1b gives us Cramer's rule for solving Ax = b. Also, the absolute value of the determinant gives the volume of a box.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 5.3 in the 4th or 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you're done.


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