sa2 - Self-Assessment 2 Math 5A, Winter 2008 By now you...

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Self-Assessment 2 – Math 5A, Winter 2008 By now you should have learned the following concepts, and should be able to answer the following questions. If you do not feel comfortable doing this, read the corresponding sections in the book, and then try to answer the questions, again without looking in the book. 1. What is a linear map? 2. What are the kernel and image of a linear map? 3. What is the dimension theorem? 4. You should be able to Fnd a basis for the kernel and image of a linear transformation, and determine its dimensions. 5. What are the eigenvectors and eigenvalues of a matrix? 6. What does it mean to diagonalize a matrix? 7. ±ind an example of a matrix that is not diagonalizable. 8. How are linear transformations and matrices related? 9. You should understand the connection between the kernel and image of a linear transformation, its rank, the existence of an inverse, the concepts of injectivity and surjectivity, and the existence of solutions to a linear system of equations. 10. Why are eigenvalues and eigenvectors important? How can you recon-
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This note was uploaded on 12/26/2011 for the course MATH 5A taught by Professor Rickrugangye during the Fall '07 term at UCSB.

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sa2 - Self-Assessment 2 Math 5A, Winter 2008 By now you...

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