Problem (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 0 1 0 P = |0 0 1 1 0 0 1 1 V3 -1 Are the three vectors v, Pv, P?v linearly independent? (ii) Consider the 4 x 4 symmetric matrix A and the vector b in R4 0 10 0 1 0 1 0 0 1 0 1 0 0 1 0 () A = 1 b = 1 Are the vectors b, Ab, A?b, A°b in R linearly independent? Show that the matrix A is invertible. Look at the column vectors of the matrix A 0000 1 1 1 Find the inverse of A.

Problem (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 0 1 0 P = |0 0 1 1 0 0 1 1 V3 -1 Are the three vectors v, Pv, P?v linearly independent? (ii) Consider the 4 x 4 symmetric matrix A and the vector b in R4 0 10 0 1 0 1 0 0 1 0 1 0 0 1 0 () A = 1 b = 1 Are the vectors b, Ab, A?b, A°b in R linearly independent? Show that the matrix A is invertible. Look at the column vectors of the matrix A 0000 1 1 1 Find the inverse of A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8AEXP

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