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Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v = V3 0 1 0 0 0 1 1 0 0 P = Are the three vectors v, Pv, P2v linearly independent? (ii) Consider the 4 x 4 symmetric matrix A and the vector b in R1 (:) - 0 1 0 0 1 A = 1 b = 0 10 1 0 0 1 0/ 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 O000 1 1 1 Find the inverse of A.

Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v = V3 0 1 0 0 0 1 1 0 0 P = Are the three vectors v, Pv, P2v linearly independent? (ii) Consider the 4 x 4 symmetric matrix A and the vector b in R1 (:) - 0 1 0 0 1 A = 1 b = 0 10 1 0 0 1 0/ 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 O000 1 1 1 Find the inverse of A.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v = V3 0 1 0 0 0 1 1 0 0 P = 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 1 0 0 1 A = 1 b= 1 1 0 1 0 0 0 1 1 0. 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 1 1 1 1 Find the inverse of A.
Transcribed Image Text:Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v = V3 0 1 0 0 0 1 1 0 0 P = 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 1 0 0 1 A = 1 b= 1 1 0 1 0 0 0 1 1 0. 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 1 1 1 1 Find the inverse of A.
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