Session Overview
Now we start to use the determinant. Understanding the cofactor formula allows us to show that A^{-1} = (1/detA)C^{T}, where C is the matrix of cofactors of A. Combining this formula with the equation x = A^{-1}b 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
- Watch the video lecture Lecture 20: Cramer’s Rule, Inverse Matrix and Volume
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
Suggested Reading
- Read Section 5.3 in the 4^{th} or 5^{th} edition.
Problem Solving Video
- Watch the recitation video on Problem Solving: Determinants and Volume
- Recitation video transcript (PDF)
- 观看视频: 习题讲解 – 行列式和体积 [watch this recitation in Mandarin]
Check Yourself
Problems and Solutions
Work the problems on your own and check your answers when you’re done.