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3. If AA'GAA' = AA' and A'AHA'A = A'A, then A'GAHA' is the Penrose inverse of A. Use this principle to find the Penrose inverse of A = 0 1 1 01 1 1 0,

3. If AA'GAA' = AA' and A'AHA'A = A'A, then A'GAHA' is the Penrose inverse of A. Use this principle to find the Penrose inverse of A = 0 1 1 01 1 1 0,

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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For this question, we are given the following information regarding the Penrose Inverse: If AA'G= AA' and A'AHA'A = A'A, then A'GAHA' is the Penrose inverse of A. Upon attempt of this question, I got the following results (attached in the question). Is my answer correct that there is no Penrose Inverse of A? If not, why?

Cuiven that Then From equation (1) Finding AA' GAA¹ = AA¹ (AA) AAGAA'= (AA¹) ¹²(AA') = I NOW So 0 0 L From equation (2) Finding value of H A'AHA'A = A'A (AA) A'AHA'A = (A'AJ¹A¹A) = I and A'AHA'A= A'A HA¹A = I HA'A) CA/A¹ = (AA) ¹ H = A²A¹) 1 Value of Grand H put in AGAMA is the pensose inverse of A AGAHA' = (A'(A') A¹A) A¹ (A¹) 'A' IA¹ I = A'GAMA = And Given that A = 1 AA & AA' = AA¹ (1) (2) A'MAHA' is the penmose inveuse of A the value of Or IGAA = I G₁(AA) (AA) ¹ = (1)(AA) ² G₁ = (A¹) ¹ = (A¹) ²¹+ At funding 11 0 0 - 0 0 0 1 0 uring augmented mateix 1 R₂R, 0 0 1 1 0 1 ooo O 1 0 10 0 L 1 Matmix A'I can't find becauve matrix A is not invectiable A'GAHA' = A1 of A. 1 we can't find penuose inveure
Transcribed Image Text:Cuiven that Then From equation (1) Finding AA' GAA¹ = AA¹ (AA) AAGAA'= (AA¹) ¹²(AA') = I NOW So 0 0 L From equation (2) Finding value of H A'AHA'A = A'A (AA) A'AHA'A = (A'AJ¹A¹A) = I and A'AHA'A= A'A HA¹A = I HA'A) CA/A¹ = (AA) ¹ H = A²A¹) 1 Value of Grand H put in AGAMA is the pensose inverse of A AGAHA' = (A'(A') A¹A) A¹ (A¹) 'A' IA¹ I = A'GAMA = And Given that A = 1 AA & AA' = AA¹ (1) (2) A'MAHA' is the penmose inveuse of A the value of Or IGAA = I G₁(AA) (AA) ¹ = (1)(AA) ² G₁ = (A¹) ¹ = (A¹) ²¹+ At funding 11 0 0 - 0 0 0 1 0 uring augmented mateix 1 R₂R, 0 0 1 1 0 1 ooo O 1 0 10 0 L 1 Matmix A'I can't find becauve matrix A is not invectiable A'GAHA' = A1 of A. 1 we can't find penuose inveure
3. If AA'GAA' = AA' and A'AHA'A = A'A, then A'GAHA' is the Penrose inverse of A. Use this principle to find the Penrose inverse of A = 0 1 1 01 1 1 0,
Transcribed Image Text:3. If AA'GAA' = AA' and A'AHA'A = A'A, then A'GAHA' is the Penrose inverse of A. Use this principle to find the Penrose inverse of A = 0 1 1 01 1 1 0,
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