Linear Transformations and their Matrices

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Session Overview

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

When we multiply a matrix by an input vector we get an output vector, often in a new space. We can ask what this "linear transformation" does to all the vectors in a space. In fact, matrices were originally invented for the study of linear transformations.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 7.1 in the textbook.

Problem Solving Video

  • Watch the recitation video on Linear Transformations (00:10:46)
  • Recitation video transcript (PDF)

Check Yourself

Problems and Solutions

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


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