Cramer's Rule, Inverse Matrix and Volume

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Session Overview

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

• Watch the video lecture Cramer's Rule, Inverse Matrix and Volume (00:51:01)

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  Cramer's Rule, Inverse Matrix and Volume

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• Read the accompanying lecture summary (PDF)
• Lecture video transcript (PDF)

Suggested Reading

• Read Section 5.3 in the textbook.

Problem Solving Video

• Watch the recitation video on Determinants and Volume (00:13:49)

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  Determinants and Volume

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• 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]

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  行列式和体积

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Check Yourself

Problems and Solutions

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

• Problems (PDF)
• Solutions (PDF)

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