Determinants Bases, linear Indep., etc Gram-Schmidt Eigenvalue and Eigenvectors Misc. 200 400 600...
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Transcript of Determinants Bases, linear Indep., etc Gram-Schmidt Eigenvalue and Eigenvectors Misc. 200 400 600...
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- Determinants Bases, linear Indep., etc Gram-Schmidt Eigenvalue and Eigenvectors Misc. 200 400 600 800
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- Find the determinant of
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- Compute
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- The axiomatic definition of the determinant function includes three axioms. What are they?
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- Suppose What is
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- Show that the following vectors are linearly dependent
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- Find the rank of A and the dimension of the kernel of A
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- Find a basis for the kernel of A and for the image of A
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- Find the equation of a plane containing P, Q, and R
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- Let Q be an orthonormal basis for the matrix S. Find the matrix of the orthogonal projection onto S.
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- Find an orthonormal basis for the image of A.
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- 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.
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- Given and Calculate q 3
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- Given A and the correspond char. polynomial, find the eigenvalues and eigenvectors of A.
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- Determine the eigenvalues and the eigenvectors of A.
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- Given A and the char. polynomial, determine: 1.The eigenvalues of A 2.The Geometric and algebraic multiplicities of each eigenvalue 3.Is it possible to find D and V such that A = VDV -1 ? Justify your answer
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- Find a diagonal matrix D and an Invertible matrix V such that A=VDV -1 Also calculate A 8.
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- Find the area of the parallelogram spanned by a and b
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- What are two methods you know for calculating the solution to a least squares regression problem which use the Gram-Schmidt QR factorization?
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- Find the area of the triangle determined by the points (0,1), (2,5), (-3,3)
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- 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