3. Let n EN with n 22 and a ER. Consider the figure (a) Show that fis linear. (b) Give the representing matrix M of f in the case n- 2. (c) For "n = 2 determine the rank of M depending on a. f: Rn + R", fi(x) = 1, + a- ran+1-i für i = 1,..., 2n [d] Let L be the set of all € R" with Show that L is a subspace of R2n is, calculate the dimension of L and find a base of L.
3. Let n EN with n 22 and a ER. Consider the figure (a) Show that fis linear. (b) Give the representing matrix M of f in the case n- 2. (c) For "n = 2 determine the rank of M depending on a. f: Rn + R", fi(x) = 1, + a- ran+1-i für i = 1,..., 2n [d] Let L be the set of all € R" with Show that L is a subspace of R2n is, calculate the dimension of L and find a base of L.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Q3 PART A
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