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Let A be a matrix with only 4 different eigenvalues 21, 22, 23, 24. It is known that: A₁ has corresponding eigenvectors u₁, U₂: A2 has corresponding eigenvectors U3, U4, 15: eigenvectors U6, U7: A3 has corresponding A4 has corresponding eigenvectors ug: Indicate if the each set below is guaranteed to be linearly independent using T or F: 1) : {4₁, 4₂}: 2) :{u₁,uz): :{u3, 2u4, 3us): :{ug, 2ug): : {u1, 3из, биб, 8ug }: : {0, ug}: :{u₁}: :{(u₁ + 2u₂), u3}: :{u₁, (u₂ + U3)}: 3) 4) 5) 6) 7) 8) 9)

Let A be a matrix with only 4 different eigenvalues 21, 22, 23, 24. It is known that: A₁ has corresponding eigenvectors u₁, U₂: A2 has corresponding eigenvectors U3, U4, 15: eigenvectors U6, U7: A3 has corresponding A4 has corresponding eigenvectors ug: Indicate if the each set below is guaranteed to be linearly independent using T or F: 1) : {4₁, 4₂}: 2) :{u₁,uz): :{u3, 2u4, 3us): :{ug, 2ug): : {u1, 3из, биб, 8ug }: : {0, ug}: :{u₁}: :{(u₁ + 2u₂), u3}: :{u₁, (u₂ + U3)}: 3) 4) 5) 6) 7) 8) 9)

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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Let A be a matrix with only 4 different eigenvalues 21, 22, 23, 24. It is known that: A₁ has corresponding eigenvectors u₁, U₂: A2 has corresponding eigenvectors U3, U4, 15: eigenvectors U6, U7: A3 has corresponding 24 has corresponding eigenvectors ug : Indicate if the each set below is guaranteed to be linearly independent using T or F: 1) :{u1,u2}: :{u₁, U3}: :{u3, 2u4, 3u5}: :{ug, 2ug}: :{u₁, 3u3, 6u6, 8ug}: : {0, ug}: :{u₁}: : {(u₁ + 2u₂), u3}: : {u₁, (u₂ + U3)}: 2) 3) 4) 5) 6) 7) 8) 9)
Transcribed Image Text:Let A be a matrix with only 4 different eigenvalues 21, 22, 23, 24. It is known that: A₁ has corresponding eigenvectors u₁, U₂: A2 has corresponding eigenvectors U3, U4, 15: eigenvectors U6, U7: A3 has corresponding 24 has corresponding eigenvectors ug : Indicate if the each set below is guaranteed to be linearly independent using T or F: 1) :{u1,u2}: :{u₁, U3}: :{u3, 2u4, 3u5}: :{ug, 2ug}: :{u₁, 3u3, 6u6, 8ug}: : {0, ug}: :{u₁}: : {(u₁ + 2u₂), u3}: : {u₁, (u₂ + U3)}: 2) 3) 4) 5) 6) 7) 8) 9)
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