?Let ???? be a square matrix.a. Show that \((I-A)^{-1}=I+A+A^{2}+A^{3} \text { if }
Chapter 1, Problem 14(choose chapter or problem)
Let 𝐴 be a square matrix.
a. Show that \((I-A)^{-1}=I+A+A^{2}+A^{3} \text { if } A^{4}=0\).
b. Show that
\((I-A)^{-1}=I+A+A^{2}+\cdots+A^{n} \text { if } A^{n+1}=0\)
Equation Transcription:
(𝐼 − 𝐴)−1 = 𝐼 + 𝐴 + 𝐴2 + 𝐴3 if 𝐴4 = 0
(𝐼 − 𝐴)−1 = 𝐼 + 𝐴 + 𝐴2 + + 𝐴n if 𝐴n+1 = 0
Text Transcription:
(𝐼 − 𝐴)−1 = 𝐼 + 𝐴 + 𝐴^2 + 𝐴^3 if 𝐴^4 = 0
(𝐼 − 𝐴)−1 = 𝐼 + 𝐴 + 𝐴^2 + ... + 𝐴n if 𝐴^n+1 = 0
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