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Determinants

Determinants. Bases, linear Indep ., etc. Gram- Schmidt. Eigenvalue and Eigenvectors. Misc. 200. 200. 200. 200. 200. 400. 400. 400. 400. 400. 600. 600. 600. 600. 600. 800. 800. 800. 800. 800. Find the determinant of. Compute.

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Determinants

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  1. Determinants Bases, linear Indep., etc Gram-Schmidt Eigenvalue and Eigenvectors Misc. 200 200 200 200 200 400 400 400 400 400 600 600 600 600 600 800 800 800 800 800

  2. Find the determinant of

  3. Compute

  4. The axiomatic definition of the determinant function includes three axioms. What are they?

  5. Suppose What is

  6. Show that the following vectors are linearly dependent

  7. Find the rank of A and the dimension of the kernel of A

  8. Find a basis for the kernel of A and for the image of A

  9. Find the equation of a plane containing P, Q, and R

  10. Let Q be an orthonormal basis for the matrix S. Find the matrix of the orthogonal projection onto S.

  11. Find an orthonormal basis for the image of A.

  12. For some matrix A, there exists Q and R as given s.t. A=QR. Solve the least squares problem Ax=b for the given b.

  13. Given and Calculate q3

  14. Given A and the correspond char. polynomial, find the eigenvalues and eigenvectors of A.

  15. Determine the eigenvalues and the eigenvectors of A. DAILY DOUBLE

  16. Given A and the char. polynomial, determine: The eigenvalues of A The Geometric and algebraic multiplicities of each eigenvalue Is it possible to find D and V such that A = VDV-1? Justify your answer

  17. Find a diagonal matrix D and an Invertible matrix V such that A=VDV-1 Also calculate A8.

  18. Find the area of the parallelogram spanned by a and b

  19. What are two methods you know for calculating the solution to a least squares regression problem which use the Gram-Schmidt QR factorization?

  20. Find the area of the triangle determined by the points (0,1), (2,5), (-3,3)

  21. In the theory of Markov Chains, a stationary distribution is a vector that remains unchanged after being transformed by a stochastic matrix P. Also, the elements of the vector sum to 1. Determine the stationary distribution of

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