H and 0 as an eigenvalue Is your matrix invertible? Is it orthogonally diagonalisable? 1. Find a matrix A with 25 as an eigenvalue with eigenvector V₁ with eigenvector V₂ =

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Publisher:Erwin Kreyszig
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1. Find a matrix A with 25 as an eigenvalue with eigenvector V₁
=
and 0 as an eigenvalue
5
with eigenvector V2
=
Is your matrix invertible? Is it orthogonally diagonalisable?
2. Let A be a 3 × 3 matrix. Assume 1 and 2 are the only eigenvalues of A.
Determine whether the following statements are always true. If true, justify why. If not
true, provide a counterexample.
Statement A: If v₁ is an eigenvector of A corresponding to 1 and v2 is an eigenvector
corresponding to 2, then A(v₁ + V₂) = 3(V1 + V2)
Statement B: One of the eigenspaces of A is two-dimensional, and the other is one-
dimensional.
MATHS 208 - Tutorial 8
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Transcribed Image Text:个 (1) 大x с Apps G 四名卤 ? →→ 个 Pano X # X X X FHE X 【× X canvas.auckland.ac.nz/courses/74445/files/8787989?module_item_id=1498328 Gmail Maps SSO MATHS 208: Gene... ACCTG 211: Finan... MATHS 208 > Files > 208 tut 8 (2022 s1).pdf 2022 Semester One Home Announcements Assignments Grades Syllabus Quizzes Modules Piazza SET Evaluations Recordings Learning Essentials Panopto Video Zoom 208 tut 8 (2022....pdf 司機X FINANCE 251: Fin... BUSINESS 202: B... 1. Find a matrix A with 25 as an eigenvalue with eigenvector V₁ = and 0 as an eigenvalue 5 with eigenvector V2 = Is your matrix invertible? Is it orthogonally diagonalisable? 2. Let A be a 3 × 3 matrix. Assume 1 and 2 are the only eigenvalues of A. Determine whether the following statements are always true. If true, justify why. If not true, provide a counterexample. Statement A: If v₁ is an eigenvector of A corresponding to 1 and v2 is an eigenvector corresponding to 2, then A(v₁ + V₂) = 3(V1 + V2) Statement B: One of the eigenspaces of A is two-dimensional, and the other is one- dimensional. MATHS 208 - Tutorial 8 Page 1 of 1 Topic 2 Exampl....docx Topic 2 SCF Can....ppt 208 tut 8 (2022 s1).pdf Download 208 tut 8 (2022 s1).pdf (105 KB) ◄ Previous Keynesian beau....docx 3240 【 X [X N Anson & Waiting's... PL ACC Shoo X Topic 1.pptx Ansv X Python - OI... Disc X Anson & Waiting -.. Cale X Next ► Peer X 208 X =S N Answers from Ans... " Update: b bartleby Show all ×
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