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