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Linear algebra proof question 1. If A is an n x n matrix, and I is the n x n identity matrix, prove 1 - A^k = (1-A)(I + A + .... + A^(k - 1)) 2. A^4 = 0, show I - A is invertible and it's inverse is I + A +A^2 + A^3

Linear algebra proof question 1. If A is an n x n matrix, and I is the n x n identity matrix, prove 1 - A^k = (1-A)(I + A + .... + A^(k - 1)) 2. A^4 = 0, show I - A is invertible and it's inverse is I + A +A^2 + A^3

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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Linear algebra proof question 1. If A is an n x n matrix, and I is the n x n identity matrix, prove 1 - A^k = (I-A)(I + A + .... + A^(k − 1)) 2. A^4 = 0, show I - A is invertible and it's inverse is I + A +A^2 + A^3
Transcribed Image Text:Linear algebra proof question 1. If A is an n x n matrix, and I is the n x n identity matrix, prove 1 - A^k = (I-A)(I + A + .... + A^(k − 1)) 2. A^4 = 0, show I - A is invertible and it's inverse is I + A +A^2 + A^3
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