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Solving Ax = 0: Pivot Variables, Special Solutions

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Session Overview

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

We apply the method of elimination to all matrices, invertible or not. Counting the pivots gives us the rank of the matrix. Further simplifying the matrix puts it in reduced row echelon form R and improves our description of the null space.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 3.2 in the textbook.

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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