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.
Lecture Video and Summary
- Watch the video lecture Cramer's Rule, Inverse Matrix and Volume (00:51:01)
Lecture 20: Cramer's Rule, Inverse Matrix and Volume
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 5.3 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Determinants and Volume (00:13:49)
Problem Solving: Determinants and Volume
- Recitation video transcript (PDF)
- 观看视频: 习题讲解 -- 行列式和体积 (00:11:33)[watch this recitation in Mandarin]
Problems and Solutions
Work the problems on your own and check your answers when you're done.