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Problem 1. (Chapter 1: 100 points) Solve Linear Algebraic Equations.

Problem 2. (Chapters 2 and 3: 100 points) Inverse, Determinant, Cramer’s Rule.

Problem 3. (Chapters 1 to 4: 100 points) Independence Tests for Functions.

Problem 4. (Chapters 1 to 4: 100 points) Independence Tests for Column Vectors.

Problem 5. (Chapters 2, 4 and 6: 100 points) Subspace Definition and Theorems.

Problem 6. (Chapter 6: 100 points) Gram-Schmidt Orthogonalization Process.

Problem 7. (Chapters 1 to 6: 100 points) Symmetric Matrices and the Invertible
Matrix Theorem.

Problem 8. (Chapter 5: 100 points) Eigenanalysis and Diagonalization.

Problem 9. (Chapter 6: 100 points) Near Point Theorem and Least Squares.

Problem 10. (Chapter 7: 100 points) Spectral Theorem and AQ = QD.

Problem 11. (Chapter 7: 100 points) Singular Value Decomposition.

Problem 12. (Chapter 4: 100 points) Linear Transformations as Matrix Multiply.

Problem 13. (Chapters 4 and 6: 100 points) Orthogonality.

Problem 14. (Chapters 1 to 7: 100 points) Fundamental Theorem of Linear Algebra.

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