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Instructions and two questions for an assignment in the mth501 course, focusing on finding bases for eigenspaces based on given matrices and eigenvalues. Students are expected to have a strong understanding of matrices, echelon form, systems of linear equations, and dependence of sets to solve the assignment. The document also includes instructions on submission and formatting requirements.
Typology: Exercises
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Maximum Marks: 20 Due Date: June 27, 2012
Please read the following instructions before attempting the solution of this assignment:
- To solve this assignment, you should have good command over 31 - 35 lectures. In order to solve this assignment you have strong concepts about following topics Introduction to Matrices. Echelon and Reduced Echelon Form. System of Linear Equation. Dependence of Sets. **Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in these lectures.
Question: 1 Marks: 10
If
, then find a basis for the eigenspace corresponding to 3.
Question: 2 Marks: 10
If
, then find the eigenvalues and a basis for each eigenspace in 2.